Petty, 26, is a former fourth-round pick of the Jets back in 2015. The Jets elected to place him on waivers after taking Sam Darnold in the first round of this year’s draft and he was later claimed by the Dolphins.
Miami waived Petty with an injury designation coming out of the preseason and he later reverted to injured reserve.
Petty is currently in the third year of his four-year, $2,833,696 contract and is set to make a base salary of $705,000 for the 2018 season.
In 2017, Petty appeared in four games and threw for 544 yards while completing 49.1 percent of his passes to go along with one touchdown and three interceptions.