Graham was cut by the Falcons on Friday, ESPN's Vaughn McClure reports.
Graham was brought into Atlanta after fellow Matt Bryant got injured last season with five games remaining. In his abbreviated stint with the team, Graham converted 11 of 13 field goal tries, which earned him the opportunity to compete with Bryant to start this season. However, following the preseason, the Falcons have apparently now opted to stick with Bryant, sending the 19-year veteran Graham packing.