The Giants also acquired running back and kick returner Darius Reynaud for an undisclosed 2011 draft pick and a conditional 2012 draft choice. The Vikings announced the deal on their website. Rosenfels and Reynaud have to pass their physicals with the Giants for the trade to be finalized.
The 6-foot-4 Rosenfels, a 10-year veteran, has passed for 4,156 yards, 30 touchdowns and 29 interceptions in 32 career games. He will likely be the second-string quarterback ahead of Rhett Bomar.
Bomar had been Manning's backup and has shown flashes of potential, but the second-year quarterback hasn't taken a regular-season snap yet.
Giants head coach Tom Coughlin said earlier Friday in a conference call with reporters that while he was impressed with Bomar's improvement throughout camp, the Giants weren't going to stop looking at other options.
Bomar had received extended snaps in camp and the final three preseason games due to Sorgi's injury and Manning's head laceration suffered against the Jets.
Sorgi was placed on season-ending injured reserve earlier this week.
Rosenfels became expendable with Brett Favre's recent return to the Vikings.
Rosenfels had an impressive preseason opener at St. Louis, completing 23 of 34 passes for 310 yards and three touchdowns. But he was just 8-for-17 for 92 yards with one TD in the next three games combined, and Vikings coach Brad Childress said after the preseason finale that Tarvaris Jackson would be Favre's backup again this season.
The move means that the Vikings likely will keep rookie Joe Webb as the third quarterback.
By obtaining Reynaud, the Giants addressed their need for help on kickoff and punt returns. They have been searching for a returner ever since losing Domenik Hixon to a season-ending knee injury earlier in the summer.
Reynaud is a converted receiver who was trying to make the Vikings as a running back and return man. He was the team's primary punt returner during the preseason. The 5-9 Reynaud finished fourth in the NFC last season with a 10.3-yard average on punt returns.
Ohm Youngmisuk covers the Giants for ESPNNewYork.com. Information from The Associated Press was used in this report.