Born in Amager, Rasmussen began his senior career at club Næstved IF. He made his debut for the Danish national team in September 1975, before he moved abroad to play professionally for Hertha BSC in the Fußball-Bundesliga. He made his Hertha debut in January 1976, and went on to play five seasons with the team, reaching two DFB-Pokal cup finals as well as winning the third place in the 1978 Bundesliga season. When Hertha were relegated to the Second Bundesliga after the 1980 Bundesliga season, Rasmussen moved back to Denmark to play for Odense BK. He played a single season at Odense, before he returned to Hertha in winter 1981, and helped the club win promotion to the Bundesliga in 1982.
Hertha were relegated once more after the 1983 Bundesliga season, and Rasmussen stayed with the club in the Second Bundesliga. He was selected to represent Denmark at the 1984 European Championship, and played two of Denmark's four games before the team was eliminated in the semi-finals. After the 1984 European Championship, he moved back to Denmark to end his career with Næstved IF. He played one further Danish national team game in September 1984, bringing him to a total of 41 games and one goal for the Danish national team.