Yes! African Americans were technically allowed to vote in the 1960's due to the 15th amendment, which was created in 1870. However, African Americans still faced a lot of discrimination in the 60's for voting; In 1965, Lyndon Johnson signed the Voting Rights Act which was aimed to overcome any barriers that African Americans still faced. After the act was enacted, voter turnout among blacks increased from 6 percent in 1964 to 59 percent in 1969. I know you said a simple yes or no but this is just for anyone who needs a more thorough answer! Hope this helps!