It was one of 11 games Thigpen -- who was acquired by the Dolphins for an undisclosed draft pick -- started for the Chiefs last season when he finished with 2,608 yards passing with 18 touchdowns, 12 interceptions and a passer rating of 76.0.
This year, Thigpen was relegated to the role of backup after Kansas City acquired Matt Cassel from New England.
Thigpen is 6-1, 224 and 25 years old, and he was a seventh-round pick of the Minnsota Vikings in 2007 who later was claimed off waivers by Kansas City.
He was the first player ever drafted from Coastal Carolina, which didn't begin playing football until 2003.
Thigpen appeared in one game as a rookie with the Chiefs in 2007 and ended the season on injured reserve after sustaining a knee injury in practice.
His older brother, Chris, played offensive guard at both South Carolina and Louisville. Thigpen's full name is Tyler Beckham Thigpen.