The New England Patriots drafted Boyce in the fourth round in 2013. He has appeared in 10 games with three starts. Boyce, 5-foot-11 and 205 pounds, has compiled nine catches for 121 yards.
He spent most of this year with the Indianapolis Colts until they waived him Aug. 16.
Parks signed with the Browns on May 20 as an undrafted rookie. He's dealing with a knee injury.