Career
Williamson played for local junior clubs Kirkintilloch Rob Roy and Petershill before signing for Rangers in 1941. He served with the Royal Navy as a PE instructor during the Second World War, while also playing for Rangers and as a guest for Manchester City. He became a regular in the Rangers first team in the 1945/46 season.
Williamson played and scored in the first Scottish League Cup final, in 1947.
Williamson scored a goal in both of those Scottish Cup finals, in 1948 and 1949. After retiring as a player, Williamson worked as a PE teacher at Lenzie Academy.