Stanton trained at NYU’s Tisch School of the Arts Graduate Acting Program and began his acting career in Joseph Papp’s production of the play Measure for Measure, at the Delacorte Theater in 1985. He was in the resident company of the American Repertory Theater in Cambridge, Massachusetts from 1989 to 1991.
His Broadway credits include John Guare’s A Free Man of Color, Friedrich Schiller’s Mary Stuart and Tom Stoppard’s The Coast of Utopia. Off Broadway credits include David Lindsay-Abaire’s Fuddy Meers, A.R. Gurney’s A Cheever Evening and Caryl Churchill’s Owners and Traps. He won an Obie Award and a Clarence Derwent Award for his performance in David Ives’s All in the Timing in 1994.
He directed an Off-Off-Broadway production of Ives’s Don Juan in Chicago in 1995.
In 2008 and 2009, he appeared in Off Broadway productions of Love Child, a two-man play that he wrote and performed with fellow actor Daniel H. Jenkins.
In March and April 2012, he appeared in the Eugene O’Neill play Strange Interlude at the Shakespeare Theatre Company, in the role of Charles Marsden.
Stanton made a brief appearance in the 1988 thriller, The House on Carroll Street. In 1992, he appeared in the films A League of Their Own and Bob Roberts. In 1993, he had what may be his most famous role, playing Henry Mitchell in Dennis the Menace.
He played John Chapman in the 1994-95 television show The Cosby Mysteries.
He later appeared in a variety of films, including Don’t Drink the Water (1994 film), Striptease, Washington Square, Red Corner, Next Stop Wonderland, Mercury Rising, The Quiet American, Head of State, The Stepford Wives, Find Me Guilty, and Confessions of a Shopaholic.
Stanton appeared in episodes of the television shows Law & Order, Law & Order: Criminal Intent, Law & Order: Special Victims Unit, Frasier, Ed, Third Watch, Damages, NYC 22, The Good Wife, and Orange Is the New Black.
He also appeared in the two sequels to Luc Besson’s Arthur and the Invisibles, playing Armand Montgomery, father to Freddie Highmore’s Arthur.