Rasmussen started his single-seater career off with Jenzer Motorsport at the opening round of the 2018 Italian F4 Championship.[2] Rasmussen completed the first ten races with 4 retirements and a best finish of 11th, a string of 3 retirements in a row starting at Monza's 2nd race left Rasmussen the only one of the 6 Jenzer drivers without a point. In race 2 at the Misano round a season best finish of 8th ended Rasmussen's points drought, things were looking good for him until the 3rd race he sustained a heavy crash with Prema driver Amna Al Qubaisi. The closest Rasmussen got to the points was a 13th-place finish, he ended the season 24th and last of his teammates.
2019
He returned for the following season but this time for Prema Powerteam and with his first race of the season he beat his entire tally from the previous year. In the second race Rasmussen was handed a ten-second penalty for overtaking under the safety car resulting in a 14th-place finish. Despite a lot of good results, including three 4th places and a pole position at Imola it took until the final round of the season for Rasmussen to take a podium where he placed 3rd in the first and third race at Monza. Before his double podium Rasmussen was 10th in the championship but ended up finishing 7th, 6 points behind his nearest competitor.[3]
ADAC F4
Rasmussen raced with Prema Powerteam in the ADAC Formula 4 in 2019.[4] The first round of the season got off to a bad start, as he retired after he sustained damage crashing into Prema teammate Paul Aron. A handful of good results and points followed before he scored a career best 2nd and first podium of the season at Zandvoort due to Dennis Hauger and Gianluca Petecof crashing in the later stages of the race.[5] Rasmussen went on to finish on the podium once more and end the season in 12th behind Paraguayan Joshua Dürksen.
He then drove for Charouz Racing System and ART Grand Prix in the post-season test, but did not sign for either team in 2022, instead switching to the FIA World Endurance Championship.[8][9][10] On 4 April 2022, however, it was announced that Rasmussen would be joining teams' champions Trident from round 2 after an ill-fated Jonny Edgar pulled out of the championship.[11] In just his first time back, he achieved his first points finish by finishing seventh.[12] He would not score any more points for the feature race and the Barcelona round.
Rasmussen was replaced at Silverstone by Edgar after the Brit recovered from his health issues.[13] Rasmussen ranked 22nd in the standings with 4 points.[14]
Sportscar career
2022: WEC debut
On 12 January 2022, Jota Sport announced that Rasmussen would join the team and drive the 28 car alongside Ed Jones and Johnathan Aberdein in the FIA World Endurance Championship.[15][16] The team started out with a fifth place at Sebring, before a retirement at Spa-Francorchamps posed a setback for Rasmussen and his teammates.[17] They would bounce back in strong fashion at the 24 Hours of Le Mans however, as the Jota 28 crew took a class podium, ending up third at the checkered flag.[18][19] Rasmussen, Aberdein and Jones scored another third place at the penultimate race in Fuji and finished sixth in the teams' standings.
2023
For the 2023 season, Rasmussen remained with Jota, being partnered by Pietro Fittipaldi and David Heinemeier Hansson.[20] Following three finishes inside the top ten during the first half of the season, the #28 crew qualified second ahead of the 24 Hours of Le Mans.[21] However, having run near the front during the evening, Rasmussen span and hit the barriers, damaging the front of his car and diminishing Jota's chances of victory.[22] Contact from another car saw Fittipaldi stranded in the gravel at the first Mulsanne Chicane four hours later, costing the team more time and leading them on to finish 13th in class.[23][24]
A highlight of the campaign proved to be the race at Monza: the team took an early lead with Heinemeier Hansson at the wheel and ran at the front for a majority of the contest, with Rasmussen executing a pass on Fabio Scherer to momentarily take third. With fellow front runners WRT having to retire thirty minutes from the end, Jota were able to win unopposed, as Fittipaldi crossed the line to give Rasmussen his first victory in sportscar racing.[25][26][27] Another podium came at the final round in Bahrain, as the #28 crew benefited from a collision the #9 Prema suffered with a GT car.[28][29] This helped the team towards a sixth place in the championship standings by the end of the year.[30]