Moss's stage career began when he acted and directed for Le Gallienne's Civic Repertory Theatre, with his first production being Peter Pan (1929).

He appeared in the original Broadway production of the Hal Prince/Stephen Sondheim musical Follies, playing impresario Dimitri Weismann.

[9] He appeared on television in Star Trek (1966) as mysterious actor Anton Karidian, alter-ego of the tyrannical Gov.

He also played in The Rifleman as the school teacher, Mr. Griswald, and as Chief Lonespear in Bonanza episode "In Defense of Honor" in 1968.

Other television appearances include The Time Tunnel, The Girl from U.N.C.L.E., The Man from U.N.C.L.E., and the anthology series The Alfred Hitchcock Hour, General Electric Theater, Alfred Hitchcock Presents, Suspense, Tales of Tomorrow, Studio One, and Kraft Television Theatre.