*Club domestic league appearances and goals, correct as of 23:00, 15 December 2024 ‡ National team caps and goals, correct as of 21:04, 21 July 2020 (UTC)
After spending two seasons in the academy he signed for FC St. Pauli in June 2016.[5][6] He became part of the reserve team, competing in Regionalliga. On 31 July he made his debut for the side, starting in the 3–1 win over 1. FC Germania Egestorf/Langreder.[7] In the return game against Egestorf/Langreder on 26 November, he scored his first goal for the team and thereby contributed to the 3–3 away draw.[8]
He was part of the first-team squad twice, but only sat on the bench for matches against SV Sandhausen and VfL Bochum.[9]
On 5 July 2018, Empoli announced that they had signed Rasmussen on a four-year contract.[13] He made his debut on 12 August in the Coppa Italia tie against Cittadella, which was lost 3–0. Seven days later he also made his debut in Serie A, in the 2–0 win over Cagliari.[14]
Fiorentina
On 31 January 2019, Rasmussen joined Fiorentina. He was sent directly to his former club Empoli on loan for the remainder of the 2018–19 season.[15]
On 21 July 2020, Rasmussen was loaned to Dutch Eredivisie club Vitesse for the 2020–21 season, with the option of extending the loan for another season.[18][19][20] During the season, Vitesse reached the final of the KNVB Cup, but lost 2–1 to Ajax. Rasmussen was sent off in the cup final.[21] A month later, the option in his loan deal was triggered, and his deal was extended by another season.[22]
On 4 November 2021, Rasmussen scored a goal and an own goal in the span of four minutes in the UEFA Europa Conference League match against Tottenham Hotspur, coached by Antonio Conte in his debut as manager of the club.[23] The match ended in a 3–2 loss for the Dutch side.[24]
Feyenoord (loan)
On 30 July 2022, Rasmussen returned to the Netherlands and joined Feyenoord on a season-long loan with an option to buy.[25] He made his competitive debut for the club on the first matchday of the 2022–23 season, starting at centre-back against his former club Vitesse in a 5–2 victory.[26] On 27 August, he scored his first goal for the club, slotting home the third goal in the club's 4–0 win over FC Emmen.[27]
Brøndby
On 14 July 2023, it was announced that Fiorentina and Brøndby had reached an agreement for the transfer of Rasmussen for an undisclosed fee, reported to be €3 million.[28] He signed a four-year contract, and was assigned the number 4 shirt.[29][30] He made his debut for the club on 6 August, starting in a 3–1 league loss to Nordsjælland.[31] On 3 September, he scored his first goal for Brøndby, easily tapping the ball in from close range to kickstart a 3–1 victory over Randers.[32][33]
^Porse, Kristian (13 September 2024). "Brøndby skifter anfører". bold.dk (in Danish). Archived from the original on 13 September 2024. Retrieved 16 September 2024.