Even though African Americans were given the right to vote in 1870 with the 15th Amendment, the Supreme Court left to the state governments the responsibility for protecting most of the basic rights of their citizens, and some state governments passed laws that made it almost impossible for African Americans, to exercise their right.. In 1965, the Voting Rights Act confirmed that no person should be denied the right to vote on account of race or color. It must be noted that the State of Wyoming granted women the right to vote in 1869. Other States followed suite. The right to vote was granted at the federal level in 1920.