Boysen has appeared for the Danish youth national team, with whom he participated in the U21 World Championship in Bosnia in 2013. He has played 15 youth national matches for Denmark. Rasmus Boysen has participated in the
EHF Cup with
Skjern Håndbold twice and once with
Ribe-Esbjerg HH. In the season - 2016/17 - Boysen secured his team
Ribe-Esbjerg HH a spot in the playoffs for the first time in the history of the club, with a goal in the last second of the home game against local rivals
SønderjyskE. They did however go on to lose both the semifinals and the bronze match. In the 2019-20 season he played for Norwegian
Elverum Håndball, where he won the
Norwegian Championship. He also has participated in the EHF Champions League with
Elverum HH. He returned a year later for familial reasons and in search of more playing time. He retired in 2022 due to suffering a
concussion during a match against
Bjerringbro-Silkeborg Håndbold. == Post playing career ==