Jenkins has a degree in drama from Illinois Wesleyan University, before relocating to Rhode Island. He worked as the artistic director of Trinity Repertory Theater in Rhode Island before breaking into film with a bit part in Feasting with Panthers (1974), a television movie.

A versatile character actor, Jenkins has steadily been working in film and television since the 1970s with other roles in Hannah and Her Sisters (1986), The Witches of Eastwick (1987), How to Make an American Quilt (1995), Snow Falling On Cedars (1999), The Man Who Wasn't There (2001) and Intolerable Cruelty (2003) He's also an occasional collaborator with the director siblings the Farrelly brothers, who have worked with Jenkins in There's Something About Mary (1998), Me, Myself, & Irene (2000), Outside Providence (1999) and Say It Isn't So (2001).

Jenkins is probably best known for his recurring role on HBO's Six Feet Under. Jenkins played Nathaniel Fisher, the deceased patriarch of the Fisher family who regularly appears to his family as a ghost, and in dreams. Jenkins played the role since the show began in 2001, through to its final season in 2005.

He recently acquired good critical notices as the blue collar mine worker dad that stands up for his daughter (Charlize Theron) in North Country.