Career
Prior to August 2012, Bjørkkjær has played for third division side, Søgne FK. Bjørkkjær also has played for the under-18 Norway national team for the U18 Lisbon International Tournament. After spending the start of the 2015 season on loan to Åsane, Bjærkkjær made his first-tier debut for Haugesund in July 2015 as a substitute against Stabæk.