Carpenter, 28, converted 91.7 percent of his field goal attempts last season, the best mark of his career. He was 25 for 25 on field goals in the second quarter or later, and he was 4 of 6 on field goals of 50 yards or longer.
The Bills signed Carpenter on Sept. 3 after rookie kicker Dustin Hopkins suffered a season-ending groin injury. After being released by the Miami Dolphins last August, Carpenter had two short stints with the Arizona Cardinals and New York Jets before signing with the Bills.
Carpenter spent the first five seasons of his career with the Dolphins, earning a Pro Bowl nod after the 2009 season.