The team was also awarded defensive end/linebacker Alex Hall off waivers from the Eagles.
Jones was recently released from the Hospital for Special Surgery and went to New Orleans to recuperate. The rookie safety has had several surgical procedures done to his left leg and foot following a car accident on June 25.
Jones will not play this season while he focuses on walking and recovering. In June, he signed a contract with the Giants worth $2.6 million for four years, with a guaranteed signing bonus of $825,000.
Hall, 24, was a seventh-round pick in 2008 by the Browns, who traded him to the Eagles in April 2010. He has three career sacks, all coming in 2008.