Dundee born inside or outside left George Stevens began his football career with hometown junior club Dundee Violet in 1909 and joined Scottish League Dundee in 1910. After a loan spell with St Johnstone in 1911 he stayed with The Dark Blues until a move to Third Lanark in 1917. After a brief return to Dundee in 1919, he moved to join North Eastern League Darlington later the same year.
On 19th January 1920 he scored both goals as Darlington caused a major Cup shock when they eliminated Football League First Division club Sheffield Wednesday from the 1920 FA Cup in front of a Monday afternoon crowd of 52,388 in a replay at Hillsborough, the first match having finished 0-0. The following season, he contributed to Darlington’s winning the North Eastern League title, thus ensuring their inclusion in the newly formed Northern Section of the Third Division. Although he didn’t play in their inaugural League fixture, Stevens helped Darlington to second place in their first season in the Football League, , scoring 14 League goals in each of the following two seasons before they went one better three years later, when they gained promotion to the Second Division as Third Division (North) Champions in 1924-25.
Together with teammate Davie Brown, Stevens was released on a free transfer at the end of the 1925-26 season after 41 goals in 142 League and Cup appearances during their League era, and he returned to the Third Division with Crewe Alexandra. The Daily Express thought their inclusion “should considerably strengthen the attack”. Brown scored heavily for Crewe, but Stevens played only rarely, and finished his League career at the end of that season after only 6 appearances.