After spending a year in Spain with the reserve team of Real Mallorca as a teenager, he spent all of his career in the lower divisions of Scottish football, playing for various clubs including Alloa Athletic (three spells), Greenock Morton, East Stirlingshire, Airdrie United, Cowdenbeath, Peterhead, and Kelty Hearts.
Stevenson only lasted just over a year at the Son Moix stadium; in his time in Spain he did not make a first team appearance but was a regular in the B side, for whom he scored a goal on his debut.
[3] Real Mallorca were keen to hold on to Stevenson and part of his release stated that he could only return to his former club Alloa, which he did in February 2004.
In the January 2009 transfer window, Stevenson rejoined Jim McInally at his new club East Stirlingshire on loan until the end of the season.
There was talk of Stevenson joining up with ex-Morton defender Ryan Harding again on the Mediterranean island of Malta to play for league champions Birkirkara[8] – this however did not materialise.