LaCosse had played in three games this season with no catches. He had three catches in two games for the Giants in 2015. LaCosse spent the 2016 season on IR.
The Giants also waived defensive tackle Khyri Thornton, who had been signed on Nov. 29. He was inactive for the two games he was with the team. Linebacker Trevor Bates was released from the practice squad.
Wide receiver Darius Powe, who broke his foot during his NFL debut on Sunday, was placed on injured reserve. Powe said he broke the foot on his first reception, but continued to play.
The Giants now have two openings on their 53-man roster. One of those could be filled by defensive end Romeo Okwara, who is on IR/Designated to Return after suffering an MCL injury.