He was born in Hansford County, Texas, the third child, and second son, of Darlene (née Deere) and James Paul Linn. In August 1969, his parents relocated the family to Oklahoma City, Oklahoma, where his father practiced law. There, he attended Heritage Hall and later Casady School, an independent school affiliated with the Episcopal Church, and was employed part-time at the Oklahoma City Zoo. It was in November 1975, after seeing Jack Nicholson in One Flew Over the Cuckoo's Nest, that Linn announced his urges for becoming an actor.
In the high school's production of Fiddler on the Roof, in which he very nearly demolished a set during a dance number, Linn was asked to leave the play by his drama coach. He was advised to direct his energy to some other field of endeavour, which effectively ended his high school acting career. He graduated from Oklahoma State University in 1980.
He began to gain recognition by playing the disgruntled and unstable Treasury agent and John Lithgow's antagonist character's second-in-command Richard Travers in the 1993 Academy Award-nominated Sylvester Stallone blockbuster Cliffhanger (opposite Michael Rooker and future Call of Duty: Modern Warfare video game trilogy voice actor Craig Fairbrass). After the success of the Stallone action thriller, he soon became a regular in Cliffhanger director Renny Harlin's later films Cutthroat Island and The Long Kiss Goodnight. In 1998, he later appear in the hit Jackie Chan and Chris Tucker action comedy, Rush Hour. He is currently most recently known in the popular TV series, CSI Miami. He also appeared in the Quentin Tarantino film, Django Unchained, reuniting with his The Long Kiss Goodnight co-star Samuel L. Jackson.