Joe Cartwright joined First Division club Manchester City in 1913 after being spotted playing for non-league Northwich Victoria. He was a bit part player in the 1913/14 season, making nine appeareances, before winning a regular berth on the left wing the following season, when he played 21 games.

He was given an opportunity with Leeds City in the 1918/19 campaign, the last year of wartime football, and made four appearances at outside-left as a replacement for Herbert Lounds. He earned good reviews for his debut, a 2-0 victory at Nottingham Forest on 8 February, with the Leeds Mercury describing him as 'admirable' and remarking that 'he and Price worked together with grand cohesion.' He could not build on a decent start, however, and quickly lost his place.

Cartwright could not command a regular first-team spot with Manchester City after the resumption of peacetime football and left to join Crystal Palace in 1921, where he remained a couple of years before ending his career in non-league obscurity with Llanelli.