According to The AP, the comedian will take the role of a "philosophical tiger" in the upcoming production of Bengal Tiger at the Baghdad Zoo.
William's character narrates writer Rajiv Joseph's dark comedy, which traces the fall of former Iraqi President Saddam Hussein.
Previews for Bengal Tiger at the Baghdad Zoo begin on March 10, with the show opening to the public on March 31.
Tony Award-nominated director Moises Kaufman will helm the play.
Williams previously appeared on Broadway in his own 2002 one-man comedy show Robin Williams Live On Broadway and acted with Steve Martin in an off-Broadway staging of Samuel Beckett's Waiting For Godot in 1988.