|Dule Hill and Jennifer Mudge in an adaption of poet Amiri Baraka's play Dutchman|
Off the top of my head, there's Langston Hughes, Maya Angelou, Sonia Sanchez, and of course Amiri Baraka. Rita Dove has written at least one play, and Cornelius Eady's Brutal Imagination had a run for an off-Broadway production. A company in Rhode Island, I recall, presented aspects of Kevin Young's Black Maria as a play.
Nikki Giovanni is not necessarily into theater, but then again, when she's on the stage for a reading, you see something that is very much like a dramatic performance. I get the same sense from some "readings" (performances) by Jessica care Moore, Saul Williams, and many others.
Beyond those direct connections, it's worth noting how many African American poets write persona poems in the voice of ex-slaves. In a way, those poets are playing or becoming those historical characters themselves. There's all kinds of drama, acting in that.
And speaking of drama and dramatic monologues, Patricia Smith's "Skinhead" where she takes on the persona of a white supremacist still continues to move folks. Baraka has a really moving piece "Dope," where he satirizes a preacher. Listening to that Baraka poem again reminds of of the amazing connections between poetry, especially black poetry and drama.