Born in Luton, Bedfordshire, Stevenson started his career in the youth system at Histon, signing for the club at the age of 15. His debut for the club came in August 2010, at the age of 18, in a 2–0 defeat to AFC Wimbledon, replacing Callum Stewart as a substitute. On 15 January 2011, Stevenson scored his first career goal in a 2–1 defeat to York City. He scored his second goal on 22 March 2011 in a 3–2 defeat to Mansfield Town Stevenson remained a regular throughout the 2010–11 season, making a total of 31 appearances, scoring two goals, but could not save Histon from relegation to the Conference North.
During the 2011–12 season, Stevenson featured in every league game for Histon, which began with a 2–2 draw against Blyth Spartans on 13 August 2011. His first goal of the season came on 6 December 2011 in a 3–0 win over Solihull Moors. Further goals in a 3–2 defeat to Gainsborough Trinity on 21 January 2012 and a 5–5 draw against Droylsden on 17 April 2012 meant Stevenson finished the season with a total of three goals. He also made two FA Cup appearances and one FA Trophy appearance to finish the season with a total of 45 appearances for Histon.
Stevenson featured in all but one league game during the 2012–13 season, making 45 appearances in all competitions once more, as he finished as top goalscorer for the club with 11 goals in his final season with Histon.