Stevenson began his career with Scottish Premier League club Aberdeen. He was released because they believed he was too small to make the grade in professional football. From there he dropped down the leagues and joined Alloa Athletic while training to become a mechanic. It was after just two first team appearances with the club that Stevenson's life was turned upside down. In what has been described as a 'Roy of the Rovers' moment he was spotted playing a game of football with his uncle on the Spanish island of Majorca. A scout from Spanish La Liga side Real Mallorca approached Stevenson and offered him a trial. Stevenson made such an impression in this trial that he was offered a 3-year contract. 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. 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.
Return to Scotland
In season 2005–06 he was a star man for Alloa Athletic almost single-handedly keeping them in the Second Division via the end of season 2nd Division/3rd Division playoffs. His form alerted several larger clubs but to many people's surprise he chose to sign a pre-contract agreement with Greenock Morton, a club who were in the same division as Alloa. Morton agreed to pay Alloa a nominal sum believed to be in the region of £16,000. In July 2008, he moved to Alloa Athletic for a third spell after joining the second division club on loan from Morton. On Hogmanay 2008 his loan spell expired, so he returned to Morton with only six-months to earn himself a new contract at the club. In the January 2009 transfer window, Stevenson rejoined Jim McInally at his new club East Stirlingshire on loan until the end of the season. It was announced that Stevenson would be released after the end of the 2008–09 season, this was confirmed by Davie Irons on the 8 May in the Greenock Telegraph. On 9 July 2009, Stevenson signed permanently for the Shire. He was released at the end of the 2009–10 season but re-signed on a one-month short term contract at the start of the following season. There was talk of Stevenson joining up with ex-Morton defenderRyan Harding again on the Mediterranean island of Malta to play for league champions Birkirkara – this however did not materialise. On 16 September 2010, he signed on a contract with Airdrie United until the end of the season. Following the expiry of his contract at Airdrie United he went on trial at SPL club Inverness Caledonian Thistle however he remained unsigned and returned to Airdrie in August 2011. In June 2012, Stevenson signed for Cowdenbeath to play in the First Division. After two seasons with Cowdenbeath, he signed for Peterhead.
