Mike Nugent is returning to New York, but he will be wearing a blue jersey instead of a green and white one this time.
The Giants had an open roster spot after rookie safety Jadar Johnson announced his retirement last weekend.
Nugent is tied with fellow kicker Nick Folk and Hall of Fame running back Emmitt Smith on the NFL's all-time scoring list with 1,052 points. He has made 236 of 292 field goals and 344 of 355 extra points in 153 career games.
Last season, Nugent made 23 of 29 field goals in 13 games with Cincinnati.