Terms of the deal were not disclosed.
The Giants were in need of a kicker because Matt Bryant suffered a right hamstring injury on a 43-yard field goal attempt on the final play of the first half in last Sunday's 23-10 loss to Miami.
Without Bryant, who is expected to miss three to four weeks, the Giants were forced to use punter Jeff Feagles in the second half against the Dolphins, and he badly missed his only field goal attempt from 29 yards.
Conway, 28, was in training camp this season with Indianapolis, but was beaten out by incumbent Mike Vanderjagt, one of the NFL's top kickers, and Conway was released before the season.
Conway spent his first five seasons with the Washington Redskins. He has made 55-of-72 field goals in 43 games, and converted 83-of-84 extra points.