Smith signed a one-year deal with the Giants before last season that netted him less than $2 million to serve as the backup to Eli Manning. He made one start and performed admirably in a Week 13 loss to the Oakland Raiders, throwing for 212 yards with a touchdown and no interceptions (but two lost fumbles). He went back to the bench when Manning was reinserted as the starter after coach Ben McAdoo and general manager Jerry Reese were fired.
The Giants signed Smith as insurance, and he beat veteran Josh Johnson for the backup position last summer.
Smith, 27, was originally a second-round pick by the Jets in the 2013 draft. His four rocky seasons with the Jets -- two as the full-time starter -- were best remembered for his broken jaw, which he suffered after being punched by then-teammate IK Enemkpali in the locker room.
At the time, Smith said he had other offers, including the potential to compete for a starting job, but he thought the opportunity to play for the Giants -- and behind Manning -- would be a valuable learning experience.
Smith has started 31 games and thrown 29 touchdown passes and 36 interceptions in five seasons. He has started just two games the past three seasons.
ESPN's Jordan Raanan contributed to this report.