In 2016, Rasmussen competed in the Danish Formula Ford Championship for Frederichsen Sport, where he finished runner-up in the standings with five wins and fifteen podium finishes. Afterwards, he the moved up to the
F4 Danish Championship, where he drove for the
Magnussen Racing Experience, where he third in the standings after winning two races and finishing on the podium twelve times. In 2018, Rasmussen moved to the United States to compete in the
Formula 4 United States Championship, joining
Jay Howard's Motorsports Driver Development. He finished third in the points after winning five races and finishing on the podium eight times. In 2019, Rasmussen remained with the now renamed
Jay Howard Driver Development and went on to compete in the
U.S. F2000 National Championship, where he finished third in the points after winning three races. He remained in the series the following year, where he won the championship, winning over half of all races and clinching the championship title at New Jersey Motorsports Park, two races before the end of the season. Across the year, he won nine races, including the first six races of the year, winning eight poles, and finished on the podium ten times. In 2021, Rasmussen remained with
Jay Howard Driver Development and went on to compete in the
Indy Pro 2000 Championship, where he won the championship after winning seven races, earning two poles, and getting twelve podium finishes. On 6 December 2021, it was announced that Rasmussen would compete in
Indy Lights for
Andretti Autosport in 2022. He finished sixth in the final points standings after winning two races at Road America and Laguna Seca. In 2023, he remained in the now renamed
Indy NXT, this time driving for
HMD Motorsports with
Dale Coyne Racing, where he won the championship after winning five races, earned five poles, and getting eight podium finishes. == IndyCar Series ==