The Dolphins will likely need a kicker for Sunday's game against the Buffalo Bills with Dan Carpenter bothered by a groin injury. Carpenter was hurt in Thursday's practice and was a limited participant in Friday's session.
Graham kicked in eight games with the New England Patriots and one with the New York Giants in 2010. He spent his first two NFL seasons with Buffalo and Carolina before a successful seven-year run with the Bengals.
After replacing an injured Lawrence Tynes for one game with New York in October 2010, he took over in New England when Stephen Gostkowski went down for the year with a thigh problem. The veteran kicked four extra points in his lone game for the Giants, then was a perfect 12-for-12 on field goal attempts for the Patriots, although he did miss two extra points.
Graham, who was in camp with the Cowboys this summer, has made 86 percent of his field goal tries in his NFL career. His best season came with the Bengals in 2007 when he connected on 31-of-34 field goal attempts and each of his 37 PATs.
The Dolphins opened a roster spot for Graham by releasing defensive back Jonathan Wade.