Following 12 goals in 15 games in the first half of the 2009–10 Superliga, Rasmussen attracted the attention of Scottish Premier League club Celtic. On 25 January 2010, Rasmussen arrived in Glasgow for contract negotiations and a medical with Celtic before signing on a three and a half year deal the next day for a fee in excess of £1 million. Rasmussen exclaimed he was delighted to join the Glasgow club saying “I started at Aarhus, before going to Brondby, which was a bigger club, so moving to Celtic is another big step up for me.” Rasmussen chose to abandon the moniker “Duncan” when playing for Celtic. He made his debut for Celtic on 27 January, coming on as a 60th-minute substitute for Georgios Samaras as the Hoops lost 2–1 to Hibernian and scored his first Celtic goal three days later in the 1–0 victory against Hamilton Accies. Rasmussen scored a goal in his third game for Celtic in a 4–2 win over Dunfermline Athletic in the Scottish Cup. On 17 April, he scored the winner in a 3–2 victory over Hibernian at Celtic Park.
Rasmussen rarely featured for Celtic under the management of Neil Lennon, making only four starts during his time with the club. He left Celtic in August 2012 after completing loan spells with Mainz, AaB and Sivasspor.
