Rasmussen began his competitive career in Denmark in 2016, racing in the Danish Formula Ford Championship for Frederichsen Sport. He finished runner-up in the standings that year, recording five wins and fifteen podium finishes. He then stepped up to the F4 Danish Championship, competing for the Magnussen Racing Experience and finishing third overall with two race wins and twelve podium finishes.
In 2018, Rasmussen relocated to the United States to contest the Formula 4 United States Championship with Jay Howard's Motorsports Driver Development outfit. He took five wins and eight podium finishes on his way to third in the championship standings. The move established him as a strong candidate for progression through the American open-wheel ladder.
In 2019, now racing for the renamed Jay Howard Driver Development team, Rasmussen entered the U.S. F2000 National Championship and finished third in points with three victories. He remained in the series in 2020 and produced a dominant championship run, winning nine races — including the first six events of the year — claiming eight pole positions and finishing on the podium ten times. He clinched the title at New Jersey Motorsports Park with two rounds still to run.
Rasmussen moved up to the Indy Pro 2000 Championship in 2021 with Jay Howard Driver Development and won the championship again, taking seven wins, two poles, and twelve podium finishes across the season. Back-to-back titles in U.S. F2000 and Indy Pro 2000 in consecutive years established him as one of the most consistent junior series performers in American open-wheel racing.
Rasmussen was announced on 6 December 2021 as a driver for Andretti Autosport in Indy Lights for the 2022 season. He won two races during the year — at Road America and Laguna Seca — and finished sixth in the final standings. In 2023, the series was rebranded as Indy NXT and Rasmussen joined HMD Motorsports with Dale Coyne Racing. He took the championship with five wins, five pole positions, and eight podium finishes, completing a full sweep of the Road to Indy ladder titles.
Rasmussen's graduation to IndyCar was announced on 25 October 2023. He drove a partial schedule for Ed Carpenter Racing in 2024, sharing the No. 20 car for selected rounds and piloting a third ECR entry at the Indianapolis 500. His best result that season was eighth place at Mid-Ohio; he finished 22nd in the overall points standings.
For 2025, Rasmussen graduated to a full-season contract with Ed Carpenter Racing. He recorded his first IndyCar victory at the Milwaukee Mile on 24 August 2025, converting his development pedigree into a maiden win at the top level of American open-wheel racing.
Rasmussen is notable for winning championships at three consecutive rungs of the American open-wheel ladder — U.S. F2000, Indy Pro 2000, and Indy NXT — before reaching IndyCar. That sequence, achieved across four consecutive seasons from 2020 to 2023, placed him among the most decorated graduates of the Road to Indy programme.
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