Annar Follesø (born December 29, 1972) is a Norwegian violinist.
Follesø studied with Soon-Mi Chung and Stephan Barratt-Due at the Barratt Due Music Institute, and with Mauricio Fuks at Indiana University. In 1998 he won the violin prize at the International Summer Academy in Salzburg for his interpretation of Bartók's solo sonata, and his Bartók interpretations have won him wide recognition. His world premiere recording of Ole Bull's violin concertos was made Record of the Year 2010 by the Grieg Society of Great Britain. Follesø records for the label 2L. Together with composer and pianist Wolfgang Plagge, Annar Follesø is artistic director of the Sunnmøre Chamber Music Festival.