Stephenson began his professional career with Joe Smith's Blackpool in November 1948. It wasn't until just over two years later, on 20 January 1951, that he made his debut in a 2–2 league draw with Sunderland at Bloomfield Road. He scored the hosts' second goal in his only appearance of the 1950–51 campaign.[3] He made three First Division appearances during the following season,[4] before injury struck, and sat out the entire 1952–53 term, at the climax of which Blackpool won the FA Cup.[5]
Stephenson returned to the Blackpool line-up two-thirds of the way through 1953–54, scoring their first goal in a 3–2 home league victory over Aston Villa on 23 January. He made seven more league appearances that season, scoring another three goals. He also scored in the FA Cup, in Blackpool's third-round replay victory over Luton Town at Molineux Stadium.[6]
He scored five goals in his eleven league appearances during 1954–55, including the only goal of the game in a victory over West Bromwich Albion at The Hawthorns on 11 December. He made his final appearance for the "Seasiders" on 15 January, in a 2–0 defeat at home to Wolves.[7]
Stephenson joined Port Vale on 10 March 1955 for £5,000.[1] He scored his first goal for the "Valiants" on 19 March, in a 2–1 defeat to Nottingham Forest at Vale Park.[1] He made a further nine Second Division appearances, without scoring any further goals, in the 1954–55 season.[1]