The income tax became available to the national government with the ratification of which amendment to the u. s. constitution?

The 16th Amendment

The 16th Amendment, passed by Congress in 1909 and ratified by a sufficient number of states by 1913, stated the following:
The Congress shall have power to lay and collect taxes on incomes, from whatever source derived, without apportionment among the several States, and without regard to any census or enumeration.

The amendment changed what had been stated originally in Article I, Section 9 of the Constitution, which had said, "No Capitation, or other direct, Tax shall be laid, unless in Proportion to the Census or enumeration herein before directed to be taken."