He first came to prominence playing in midfield for Scottish First Division side Clyde, but was converted to striker when he signed for Aberdeen, forging a prolific partnership with Joe Harper. After winning the Scottish Premier Division title in 1980, he had a four year spell with London club Tottenham Hotspur, where he won FA Cup winners medals in 1981 and 1982 and the UEFA Cup in 1984.
Archibald scored 77 goals in 189 appearances for Spurs between 1980 and 1984, forming successful striking partnerships with Garth Crooks and Mark Falco. He was a member of the Scottish national team at the 1982 and 1986 World Cups. In 1984 he joined Barcelona, where he was a popular figure until restrictions on fielding foreign players led to him being excluded from the squad in favour of Gary Lineker and Mark Hughes. He was loaned out to Blackburn Rovers for a spell prior to a surprise return to Scottish football with Hibernian. After a brief return to Catalonia with RCD Espanyol, he joined St Mirren and was influential in bringing former Barça teammate Victor Muñoz to the club.
Archibald’s later career saw him make a handful of appearances at a number of clubs in Scotland, England and Ireland, including a nostalgic return to Clyde. In 1994 he joined East Fife as player-manager.