Rømer started playing football for Køge Boldklub alongside his brother Marcel, before moving to the FC Midtjylland academy as a 15-year-old.
[4] Rømer made his Danish Superliga debut on 9 December 2012 in a 2–0 win over AC Horsens, where he came on as a substitute in the 90th minute for Petter Andersson.
[8] He played a total of 22 league matches and scored one goal, with an additional two cup appearances during the 2013–14 season.
[9][6] During the season, Rømer made his UEFA Europa League debut in the play-off round against Greek club Panathinaikos.
[17][18] Rømer made his debut on 28 February 2021 in a 4–1 win over Utsiktens BK in the Swedish Cup, where he played alongside fellow Danes Jeppe Okkels and Frederik Holst.