Will I be able to join the coast guard with a history of anxiety disorder?

Depends. Anxiety disorders cover a broad spectrum of conditions of varying severity. See http://cpancf.Com/anxietydisordersbasics.Asp for an overview. If mild and resolved it may not be an automatic disqualification. There may be a request to treating providers for furhter information or reassurance it would not be problematic. Obviously stress tolerance and function is important in such careers.