The 6-foot-2, 265-pound Maponga, who was signed Saturday, was a fifth-round draft pick (153rd overall) out of TCU by Atlanta in 2013.
Maponga played in 24 games with the Falcons - 12 each in 2013 and 2014 - before being waived by the Falcons before the start of the 2015 season.
In his career, Maponga has recorded eight tackles and a sack, which was for an 11-yard loss against Tampa Bay last season. He recovered two fumbles in 2014.
Maponga was born in Zimbabwe and grew up playing rugby until coming to the United States as a 9-year-old.
The Giants had an opening on the roster after waiving third-year defensive end Damontre Moore on Friday.
The Giants play Monday night at Miami.