Four. Three have played in the AFC Championship game, and one in an NFC Championship game.
1999 - Shaun King, Tampa Bay Buccaneers
2004 - Ben Roethlisberger, Pittsburgh Steelers
2008 - Joe Flacco, Baltimore Ravens
2009 - Mark Sanchez, New York Jets
No rookie QB has ever played in a Super Bowl.
Hat tip to Scott Kacsmar (@CaptainComeback) for the stats.