Early on in his football career, Dawson played for non-league sides Whitley Athletic and North Shields before moving to Scottish club Heart of Midlothian in 1911. In 1913, however, Hearts were required to sell Dawson in order to fund improvements to their Tynecastle Stadium, and he was transferred to Blackburn Rovers for a fee of £2,500 - a fee which several sources claim was a then world record transfer fee. The outbreak of World War in 1914 brought about an end to professional football in Britain, however, Dawson returned to Blackburn after the war and remained with the club until 1922.
Dawson played four matches for Barrow in 1923 before retiring from football.