Craig will be a recurring cast member in the show, which features Campbell Scott and Hope Davis. Her first appearance will be on Sept. 28.
Craig plays Marcy Park in Spelling Bee, and was among winners of a Drama Desk Award for Best Ensemble.
Her other credits include Sung Rno’s WaVe, Pericles, Fuenteovejuna and The Karaoke Show.
"6 Degrees" gets it title from the John Guare play Six Degrees of Separation, which puts forth the theory that all human beings are connected to one another by anywhere from one to six people.