The Giants were in need of a kicker when Matt Bryant suffered a right hamstring injury after making a 43-yard field goal 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 at kicker in the second half against the Dolphins. He badly missed his only field goal attempt from 29 yards.
Conway, 28, was in camp with the Indianapolis Colts. But with Mike Vanderjagt, one of the NFL's top kickers in Indianapolis, Conway was released before the season.
Conway spent his first five seasons with the Washington Redskins and has made 55-of-72 field goals in 43 games. He also has converted 83-of-84 extra points.