Wrap material supply systems for delivering wrap material from a wrap material roll for application around crop bales include a baler housing containing a baling chamber, a drive roll rotatably mounted to the baler housing, and a pivoting frame coupled to the baler housing at a first pivot point. A feed roll is rotatably mounted to the pivoting frame and positioned to engage the wrap material roll. The wrap material supply system further includes a drive belt, which, when tensioned, transmits rotation from the drive roll to the feed roll. An actuator is controllable to rotate the pivoting frame about the first pivot point to move the feed roll relative to the drive roll, tension the drive belt, and initiate feeding of the wrap material from the wrap material roll into the baling chamber.