Joseph "Joe" Cartwright was an English professional rugby league footballer of the 1920s, playing at representative level for Great Britain, and England, and at club level for Leigh, as a Hooker, i.e. number 9, during the era of contested scrums. Cartwright was selected to go on the 1920 Great Britain Lions tour of Australasia. He won caps for Great Britain while at Leigh in 1920 against Australia, and New Zealand, and in 1921-22 against Australia. and won caps for England while at Leigh in 1921 against Wales, Other Nationalities, and Australia, in 1922 against Wales, and in 1923 against Wales,