He first began playing football at the small club of Leiknir, before he started practicing at KR Reykjavík, Iceland's largest club. He spent most of his youth career at KR Reykjavik. His skill attracted interest from foreign clubs, and he eventually went to the Swedish club of Örgryte IS in 1995. Halfway through the season, he moved to Lillestrøm SK in Norway. Rúnar was a success there, and moved to K.S.C. Lokeren Oost-Vlaanderen in Belgium in 2000.