OECD Corporate Tax Rates. Statutory rates for 2012 and effective from 2006-09. Source: Organisation of Economic Co-operation and Development, "Taxation of Corporate and Capital Income," oecd.org, 2012
The creation of the federal corporate income tax occurred in 1909, when the uniform rate was 1% for all business income above $5,000.  Since then the rate has increased to as high as 52.8% in 1969.  Today's rate is set at 21% for all companies.  Throughout US corporate tax history, Americans have debated whether or not lowering the rate results in job creation.
Proponents of lowering the corporate tax rate to create jobs argue that it incentivizes job creation in the United States instead of overseas, encourages increased investment in research and infrastructure, and passes savings on to consumers through lower prices. They say that the United States already has the highest corporate income tax rates in the world, which creates a competitive disadvantage for US businesses.
Opponents of lowering the corporate tax rate to create jobs argue that it results in more profits for corporations without affecting job creation, and that unemployment rates were the lowest in recorded US history during the time when corporate income tax rates were highest. They say that lowering the rate would increase the US deficit, and that companies hire employees based on need, not because of corporate tax rates.
The first federal income tax was levied by Congress from 1862-1872 to pay for the Civil War, but was replaced by a tariff (a tax on imported goods that raises prices for consumers to advantage domestic producers). The federal income tax (a 2% flat tax on incomes above $4,000, including corporate income) was revived by Congress in the Income Tax Act of 1894, which the Supreme Court declared unconstitutional in 1895 in Pollack v. Farmers’ Loan & Trust. In a 5-4 decision, the justices ruled that federal taxes on personal income are "direct taxes," a class of taxes that Article I, Section 2, Clause 3 of the Constitution requires be "equally apportioned among the states according to population." According to the Wall Street Journal, imposing personal income taxes equally among states is "obviously impossible," because state populations vary widely and fluctuate from year to year. 
Since corporate income taxes were considered "excise" taxes (taxes on the sale, or production for sale, of specific goods), the Supreme Court’s ruling did not apply to them.  In a June 16, 1909 address to Congress, President William Howard Taft proposed simultaneous actions: a constitutional amendment allowing the federal government to levy a personal income tax and a separate federal tax on corporate income.  The Corporation Excise Tax Act of 1909 imposed a 1% tax on corporate income above $5,000.  On Feb. 3, 1913, Congress passed the 16th Amendment, giving Congress the "power to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several States…" 
From 1909 - the first year the federal government levied a separate corporate income tax - to 1935, corporations paid a fixed percentage of their income in taxes regardless of how much they made (although taxes were usually exempted for the first several thousand dollars). From 1936 to today, the number of federal corporate income tax brackets has varied from one to eight. Corporations today pay a 21% tax rate on income, regardless of their size or revenue. 
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Number of pages of federal tax code, 1913-2012. Source: "2012 CCH Whole Ball of Tax," CCH.com (accessed June 15, 2012)
Corporate income taxes rose from 12.4% of total government receipts in 1996 to 15.6% in 2006, before declining again to 11.6% in 2016. 
The US unemployment rate for persons 16 years of age and older rose from 3.9% in 1947 (the first year data are available) to 6.8% in 1958. The rate steadily declined to 3.5% in 1969, but then rose to a historical peak of 9.7% in 1982. The unemployment rate declined again to 4% in 2000, and it increased again to 9.6% in 2010 before declining once again to 4.4% in 2017. 
The United States, in 2016, had the highest top federal corporate income tax rate in the OECD at 35%, with France (34.4%), Belgium (33%), Mexico (30%), Australia (30%), Greece (29%), Portugal (28%), New Zealand (28%), Italy (27.5%), and Israel (25%) rounding out the top ten.  Even after accounting for additional state-level corporate income tax rates, the United States remained on top (38.9%).  Since 1997, 30 of the Organization of Economic Cooperation and Development (OECD) member counties have lowered their statutory (written) corporate income tax rates, creating an average tax burden of 25.1%. 
Businesses, however, rarely ever pay the statutory corporate income tax rate, due to a wide variety of tax exemptions, preferences, and deductions. The "effective tax rate" is defined as the "ratio of tax paid to pre-tax profits for a given period," according to the Tax Foundation. Effective tax rates, therefore, measure "the real tax cost of investment and reflect the corporate tax burden."  In 2011, the effective corporate tax rate in the United States was 29.2% (including state and local taxes), roughly in line with the 31.9% average of the six other largest developed economies (Canada, France, Germany, Italy, Japan, and the UK), and fourth highest among the 34 OECD countries.  Of the 500 large cap companies (a market capitalization value of more than $10 billion) in the Standard & Poor (S&P) stock index, 115 paid a total corporate tax rate – federal and state combined – of less than 20% from 2006-2011, and 39 of those companies paid a rate of less than 10%. 
From 1909 through 1945, Congress consistently raised the corporate income tax, and despite a brief decrease from 1945-1952 to encourage business growth following World War II, continued to raise it through 1978. In 1942, in the midst of World War II, US President Franklin Roosevelt said "when so many Americans are contributing all their energies and even their lives to the nation's great task, I am confident that all Americans will be proud to contribute their utmost in taxes."  From 1940 to 1942 alone, Congress passed four separate Revenue Acts which raised top marginal corporate income tax rates from 19% to 40%. 
President Lyndon Johnson, citing the need to approve "a sensible course of fiscal and budgetary policy" and unwilling to gut his comprehensive entitlement programs to pay for the Vietnam War, signed into law the Revenue and Expenditure Control Act of 1968.  This act created a temporary 10% income tax surcharge on corporations and increased the top marginal tax rate from 48% to 52.8%.  Congressional Chair of the House Ways and Means Committee and fiscal conservative Wilbur Mills (D-AR), an ardent skeptic of corporate tax increases, called the act "fiscal activism” and agreed to its passage only after a concurrent 10% cut in federal discretionary spending. 
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Corporate tax revenue as a percentage of GDP, 1950-2010. Source: Michael Diedrich, "Graph of the Day: Jobs and Taxes," mn2020hindsight.org, Oct. 20, 2011
The 1980s saw four major changes to federal corporate income taxes. The most consequential change, the Tax Reform Act of 1986, reduced the number of corporate income tax brackets from seven to five and slashed rates for all businesses while eliminating $30 billion annually in corporate tax loopholes.  Bill Bradley, a Democratic Senator from New Jersey who worked to pass the legislation, said that "the trade-off between loophole elimination and a lower top rate became obvious (the lower the rate, the more loopholes had to be closed to pay for it)… The bipartisan coalition produced a bill that... led to more… economic competitiveness."  Former Republican Senator Alan Simpson, in a statement blasting the act, stated that "the tax reform of 1986 [closed] loopholes that resulted in the largest corporate tax hike in history… Reagan raised taxes 11 times in eight years!"  From Oct. 1986, when the Tax Reform Act of 1986 lowered the top marginal corporate income tax rate from 46% to 34%, to Aug. 1993, when rates were increased on businesses earning over $10 million, the federal unemployment rate remained at 6.6%. 
On Aug. 10, 1993, President Bill Clinton signed into law the Omnibus Budget Reconciliation Act, which created four new corporate tax brackets with increased rates for businesses with incomes over $335,000.  Vice President Al Gore, in a statement hailing the bill’s passage, said "[This bill] means jobs, growth, tax fairness… It’s a message of hope to the small business owner and 96% of all small businesses who will get a tax cut under this plan."  The bill was attacked by United States Chamber of Commerce President Richard Lesher, who said that the corporate tax increases would "slow economic growth and fuel inflation..." and that "foreign competitors would gain an economic advantage over American goods here and abroad."  A group of 300 major corporations and trade associations known as the Tax Reform Action Coalition said it "strongly opposed Mr. Clinton’s move to increase the top rates for… corporate taxes."  From the passage of the bill until the end of Clinton’s term, the US economy gained more than 21.4 million jobs, the unemployment rate fell from 6.8% to 3.9%, industrial production rose by 5.6% per year, and the Dow Jones Industrial average rose 26.7% per year. 
In Oct. 2017, House Republicans proposed a new tax plan supported by the Trump administration, the Tax Cuts and Jobs Act, that would cut the corporate tax rate from 35% to 20%, effectively an $845 billion corporate tax cut.  On Dec. 22, 2017, President Trump signed into law an amended version of the Tax Cuts and Jobs Act, introducing a single corporate tax rate of 21%, that took effect on Jan. 1, 2018.  According to a Jan. 28, 2019 National Association for Business Economy survey, 4% of businesses increased hiring because of the 2017 Tax Cuts and Jobs Act. 
According to a Sep. 27, 2017 Pew Research Center poll, 52% of Americans believe that tax rates on large businesses and corporations should be raised and 24% believe the rates should be lowered.