Yes, specific phobia is an anxiety disorder. Specific phobia is an extreme fear of a specific object or situation. The feared simulus is avoided at all cost, and if it can't be avoided, it is endured with extreme anxiety and fear. Specific phobia is an anxiety disorder as it involves irrational thinking, extreme anxiety symptoms, and avoidant behaviors...all significantly impacting the afflicted person's life, relationships, and school or job.
Watch the following video on how specific phobia develops, and how it can be treated: