Born in Kirkintilloch, Dunbartonshire, Storrie began his senior career as a teenager at Airdrieonians, after playing alongside Willie Wallace at Kilsyth Rangers. He made his debut in the 1957–58 season, before being signed by Don Revie for Leeds United as a proven goalscorer for a fee of £15,000 in 1962. He scored the only goal on his debut in Leeds opening match of the 1962–63 season and went on to help Leeds win promotion to the First Division in the 1963–64 season, and to reach the 1965 FA Cup Final. Injuries reduced his first team opportunities and he faded out of the first team before joining Aberdeen in February 1967. He later played for Rotherham United, Portsmouth, Aldershot and St Mirren.