After making his Broadway debut in a 2003 revival of Big River, Kotsur's performance in a 2012 production of Cyrano earned him a nomination for the Ovation Award for Best Actor in a Play.

He directed and starred in the film No Ordinary Hero: The SuperDeafy Movie (2013) and gained wider attention with his guest role in the Disney+ series The Mandalorian (2019).

[5] When Kotsur received an acting job offer from the National Theatre of the Deaf, he accepted it and left Gallaudet to tour with NTD for two years, performing in two plays.

[5] On stage, his roles included Stanley in A Streetcar Named Desire, Lenny in Of Mice and Men, and Prince Hamlet in Ophelia.

[6] In 2001, Kotsur and hearing actor Lyle Kanouse were cast together in a Deaf West Theatre production of the 1985 musical Big River.

[11][12] In 2021, Kotsur appeared in the feature film CODA in a supporting role as the deaf father of a hearing teenage daughter.

Director Sian Heder first saw his performances in Deaf West productions of Our Town and Edward Albee's At Home at the Zoo and cast him as part of the ensemble.