Ahead of the 2011–12 season, Annan was linked with a move to Russian side Spartak Moscow. Instead, Annan opted to join Eredivisie side Vitesse Arnhem on a season-long loan deal. Annan made his Vitesse debut on 10 September 2011, where he played the whole game and made his first start, in a 4–0 loss against AZ Alkmaar. Since making his debut, Annan established himself in the starting eleven at the club until he called up by the national squad for the Africa Cup of Nations. After the campaign of the African Cup of Nation finished, Annan returned to the first team and made a handful of first team appearances before suffering an abdominal influenza that kept him out for the rest of the season. While the club was in doubt about signing Annan for the next season, he nevertheless returned to his parent club.