African-American men received the right to vote in 1870, as a result of the 15th Amendment to the constitution. But women (both black and white) did not receive the right to v … ote until the 19th amendment was finally ratified in August 1920.ome states allowed free Blacks to vote early in US history, most did not. The post-Civil War amendments outlawed state and fed rules forbidding voting by race. The US Constitution granted African-American men the right to vote under the Fifteenth Amendment in 1870.