Watson excelled at association football while at school, playing as a full back on either flank. While at university, he became an amateur player for Maxwell F.C. before signing for Parkgrove F.C. in 1876 where he also became the match secretary. During the 1880s he played for and was secretary of the prestigious Glasgow club, Queen’s Park. During his time there, Queen’s Park won a number of Scottish Cup finals.
On 12th March 1881, Andrew Watson received his first Scotland cap in a game against England at Kennington Oval in London. He captained his side to a 6-1 victory. He represented his country on two other occasions, against Wales a few days after his début, and again facing England a year later at Hampden Park in Glasgow. Scotland won both matches 5-1.
In 1882 he joined Swifts F.C., a team based in Slough, England where he became the first black player to compete in the F.A. Cup. Two years later he transferred to the elite Corinthians team. Following the end of his footballing career Watson emigrated to Australia where he died just after the turn of the century.