Graham, who kicked for Buffalo and Carolina in his first two NFL seasons before a seven-year run with the Bengals, appeared in just one game for the Giants last October before signing with New England in November.
The 10-year 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 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 Cowboys now have four kickers on their roster, including David Buehler, who last year made 24-of-32 field goal attempts and finished with 114 points.
On Tuesday the Cowboys also released long snapper Corey Adams, wide receiver James Cleveland and running back Frank Warren.