Is there any law in the United States that says it's people have to pay Federal Income Tax on their earnings?

Title 26 of the U.S. Code is the codification of the Internal Revenue Code which was passed by Congress and signed into law by a President.
http://www.law.cornell.edu/uscode/uscode...
The actual Internal Revenue Code can be seen in the U.S. Statutes at large available at most Federal Depository Libraries. Many large state universities will be an FDL and some public libraries.

Article 1 Section 8 of the Constitution provides Congress with the power to lay an income tax. Amendment 16 clarified that power because the Supreme Court in 1895 got the constitutional intent wrong.

If someone told you that wages or earnings shouldn't be taxed because it is a fair trade for your labor is wrong. There have been hundreds of court cases where the tax protestor has brought this argument. My favorite is U.S. v Koliboski 732 F.2d 1328, 1329 n.1 (7th Cir. 1984) where the court said...
鈥淎lthough not raised in his brief on appeal, the defendant鈥檚 entire case at trial rested on his claim that he in good faith believed that wages are not income for taxation purposes. Whatever his mental state, he, of course, was wrong, as all of us are already aware. Nonetheless, the defendant still insists that no case holds that wages are income. Let us now put that to rest: WAGES ARE INCOME."

Actually, no, there is not. The "why" that we do so anyway is that the IRS has the legal clout, with the court's backing, to make people obey.
Amendment 16 of the Constitution

Though - the amendment was never rightfully and legally ratified, the President and Attorney General signed off and declared it as such

Off from this came the IRS Code that has been adjucated as legal and binding
Yes there is. It is called the "law of probablity". You dont pay...the IRS will "probably" hunt you down and split you from crotch to eyeball with a dull deer antler...
ooooooooohhhhhhh you think the government is stealing from you. LOL a law?? join the club. you never heard the saying...the only sure thing in life is death and taxes? it's not a limerick, it's fact.
Of course there is! Just like there's a law that says you have to have a driver's license to drive a car and another one that says you can't drive drunk or carry a gun in a school.

The law that covers the Federal Income Tax is Title 26 of the US Code. (The 16th amendment allowed income taxes to be treated as indirect taxes without apportionment but is not the law that says you have to pay income taxes.)

Here's a link to Title 26: http://www2.law.cornell.edu/uscode/26/us...
I wish Yahoo answers would ban this tired old question. Yes, you are required to pay taxes if you have enough taxable income. Try either not filing a tax return if you have earnings, or filing a tax return with being a tax protestor, and you will find out very quickly what exact laws require you to pay taxes. You'll get a nice, or not so nice, letter from the IRS telling you what you owe, and what laws require you to pay taxes. Also, better set some money aside to pay penalties and interest and fines on top of the taxes.