Groy fills an immediate need after being signed off the Tampa Bay Buccaneers practice squad Wednesday. Starting right guard John Miller is out indefinitely with a high left ankle sprain sustained in a 20-13 loss at New England on Monday.
Groy had three starts in four games as a rookie last year in Chicago.
Thigpen, who doubles as a kickoff returner, was a free agent. He rejoins Buffalo after being cut by the team last month.
To make room on their roster, the Bills released running back Dan Herron and receiver Denarius Moore.
Buffalo travels to play at Kansas City on Sunday in a key AFC matchup between two teams with 5-5 records.
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