Parsons, 83, won an Oscar for her work in "Bonnie & Clyde." Her television credits include "Roseanne" and "All in the Family."
She will co-star with Tate Donovan and Frances McDormand in the world premiere of playwright David Lindsay-Abaire's drama, which is being directed by Daniel Sullivan.
Preview performances are to begin Feb. 8. Opening night is scheduled for March 3.
"Welcome to Southie, a Boston neighborhood where a night on the town means a few rounds of Bingo … where this month's paycheck covers last month's bills … and where Margie Walsh has just been let go from yet another job," a synopsis of the play said. "Facing eviction and scrambling to catch a break, Margie thinks an old fling who has made it out of Southie might be her ticket to a fresh new start. But is this apparently self-made man secure enough to face his humble beginnings? Margie is about to risk what little she has left to find out."