Graham joins David Buehler, Dan Bailey and Kai Forbath on the roster. However, Buehler (hip) and Forbath (quadriceps) are injured. Bailey handled the kicking duties in Sunday's preseason game vs. the San Diego Chargers but did not have a field goal attempt.
Graham was cut by the Washington Redskins after missing field goal tries from 29 and 49 yards in the first week of the preseason. He went 12-of-12 last year with the New England Patriots after replacing Stephen Gostkowski.
"I know I'm better than the game I had with the Redskins," Graham said Tuesday. "I'm confident. I came in here and had a good workout in front of the coaches and everybody, and I don't think they would have signed me if they weren't confident in me. I just want the opportunity to do well."
Graham spent most of his career with the Cincinnati Bengals (2003-09) but also has had stops with Buffalo Bills, Carolina Panthers and the New York Giants. For his career he has made 208 of 242 field goal attempts (86 percent). He has 48 career touchbacks, however, with the kickoffs moved to the 35 this year that figure could improve.
It is not clear when Buehler will be able to return. He suffered the injury in practice last week. He is a weapon as a kickoff specialist but has not been consistent on field goals. Bailey has had a better percentage in camp than Buehler but has struggled more lately in camp. Forbath is on the non-football injury list and has yet to kick.
Todd Archer covers the Cowboys for ESPNDallas.com.