Brownhills, Staffordshire born outside left George Dorsett started his football career with Shireoaks Athletic in 1898 and joined Brownhills Albion in 1900, from where he signed for Second Division West Bromwich Albion in 1901, making his Football League debut at Preston North End in January 1902. He scored once in 17 appearances as Albion won promotion to the First Division as Second Division Champions. Despite their relegation in 1904, when he was an ever present in the campaign, Dorsett stayed with Albion until he was signed by Manchester City in January 1905 after 22 goals in exactly 100 games for The Baggies.
He spent the rest of his career at Hyde Road, making his last appearance in February 1912 before his retirement and that included another Second Division Championship medal as City bounced straight back from relegation to win the 1909-10 title, when he was an ever present, scoring 14 goals during the campaign. Dorsett started playing at left half from September 1909 and mainly featured at wing half thereafter. In total he scored 65 goals in 211 appearances at City, which included a hat-trick in a 3-2 win over Aston Villa in March 1908.
His younger brother Joe also played for West Bromwich Albion and Manchester City, and they played together at City. His nephew, Dickie Dorsett, played for Wolves and Aston Villa both sides of the Second World War.