Araiza has been out of the NFL since being released by the Buffalo Bills last August, two days after a lawsuit was filed accusing him and two former San Diego State teammates of being involved in an alleged gang rape of a 17-year-old girl.
Araiza might not have a clear path to a roster spot with the Jets, who signed veteran punter Thomas Morstead last month and gave him a $1.1 million guarantee on a $1.3 million contract.
The San Diego district attorney decided late last year to not press criminal charges against Araiza, and San Diego State announced last week that an internal investigation found no wrongdoing by Araiza. The school also said none of the former students named in the lawsuit is the subject of a current investigation, although it reserved the right to "reinstate" an investigation if there are new developments.
Araiza, who was 21 at the time of the alleged incident, has maintained his innocence. The civil case remains ongoing in the matter.
ESPN's Alaina Getzenberg and Rich Cimini contributed to this report.