The 15th Amendment to the Constitution granted African American men the right to vote by declaring that the right of citizens of the United States to vote shall not be denied or abridged by the United States or by any state on account of race, color, or previous condition of servitude..he House of Representatives passed the 15th Amendment on February 25, 1869, by a vote of 144 to 44 The Senate passed the 15th Amendment on February 26, 1869, by a vote of 39 to 13. The text of the 15th Amendment can be found in the United States Statutes at Large, volume 16, page 346 (15 Stat. 346).