Starting as a centre forward, Stevenson began his career with hometown Scottish League First Division club Airdrieonians.

[1] Stevenson moved to England to sign for Third Division South club Brentford during the 1927 off-season.

[3] Stevenson lost his right back position to new signing Jack Astley during the 1933–34 season and made just three appearances before departing the club at the end of the campaign.

[4] Stevenson moved to Northern Ireland for a spell with Irish League club Ards, managed by former Brentford full back partner Tom Adamson.

[2] He ended his career back in Scotland with Highland League club Ross County.