Randolph County is a county on the central eastern border of the U.S. state of Alabama. As of the 2020 census, the population was 21,967. Its county seat is Wedowee. Its name is in honor of John Randolph, a member of the United States Senate from Virginia. Randolph County was a prohibition or dry county until 2012, when the citizens of Randolph …Randolph County is a county on the central eastern border of the U.S. state of Alabama. As of the 2020 census, the population was 21,967. Its county seat is Wedowee. Its name is in honor of John Randolph, a member of the United States Senate from Virginia. Randolph County was a prohibition or dry county until 2012, when the citizens of Randolph County voted to repeal prohibition.