Yes, there is a Blue Exorcist movie and an OVA (Original Video Animation). The movie, titled "Blue Exorcist: The Movie" or "Ao no Exorcist: The Movie," was released in December 2012 in Japan. The OVA, known as "Blue Exorcist: Kyoto Saga OVA," was released in April 2017 and serves as an additional episode to the second season.