The income tax is authorized by the Sixteenth Amendment to the Constitution of the United States, which provides:

Tax protestors love to quote some old Supreme Court opinions that say that the Sixteenth Amendment "conferred no new power of taxation." Stanton v. Baltic Mining Co., 240 U.S. 103 (1916); see also Brushaber v. Union Pac. R. Co., 240 U.S. 1 (1916).

Because an income tax was declared unconstitutional before the adoption of the 16th Amendment in a case called Pollock v. Farmers’ Loan and Trust Co., 157 U.S. 429 (1894), on reh’g 158 U.S. 601 (1895), and because the 16th Amendment conferred no new power of taxation, protestors conclude that the income tax must still be unconstitutional.

This conclusion is false. The short answer is that, while the Supreme Court did hold that the 16th Amendment conferred no new power of taxation, the amendment relieved the pre-existing power to tax incomes from the constitutional requirement of apportionment. Therefore, the previous problem with the income tax was removed and the income tax is now constitutional.

Here's some more detail:

Congress's power to "lay and collect taxes" is given in Article I, section 8 of the Constitution. This power, given in the original Constitution, included the power to lay and collect income taxes. In Brushaber, one of the very cases the protestors love to quote, the Supreme Court said that the power to impose income taxes was "an authority already possessed and never questioned." Brushaber v. Union Pac. R. Co., 240 U.S. 1, 17 (1916).

But, according to the Pollock case, certain income taxes were subject to another provision of the original Constitution that required "direct taxes" to be apportioned among the states according to the census.

The Sixteenth Amendment overruled the Pollock case. As the Supreme Court said in Brushaber, "the Amendment was drawn for the purpose of doing away for the future with the principle upon which the Pollock Case was decided". The Amendment, the Court said, "provides that income taxes, from whatever source the income may be derived, shall not be subject to the regulation of apportionment."

Thus, the Sixteenth Amendment gives no new power to tax incomes, because that power always existed, but it relieves the pre-existing power from the requirement of apportionment. Income taxes are now constitutional because they are no longer subject to the apportionment requirement.

That is the true meaning of the statement that the Sixteenth Amendment gives "no new power of taxation." That statement does not show the income tax to be unconstitutional.