Ghana national football team
In November 2013, coach Maxwell Konadu invited Annorbaah to be a part of the Ghana national football team squad for the 2013 WAFU Nations Cup. He helped the Ghana national football team to a first place finish after the Ghana national football team beat Senegal national football team by three goals to one. Annorbaah was part of the Ghana national football team squad that finished runner-up at the 2014 African Nations Championship.