He was needed because the record-setting Tiki Barber retired at the end of last season.
In 2006, Droughns, a former Oregon product and seven-year NFL veteran, scored four touchdowns on 220 carries for 758 yards.
For his career, the 5-foot-11 inch, 220-pounder has 13 scores on 844 carries for 3,327 yards while playing for Cleveland, Denver, and Detroit.
In the trade, the Giants parted with wide receiver Tim Carter.
Droughns became expendable when the Browns signed free agent Jamal Lewis earlier this week.
Carter, a five-year veteran, had 22 catches for two touchdowns and 253 yards last season.
For his career, Carter has 72 receptions for 967 yards and three scores.