Ron Jaworski is a distant cousin, but as I haven't seen him since a family reunion in Scranton almost four decades ago, technically I've never run into a pro athlete.
Interestingly enough, he's arguably not even the best quarterback in the clan: Another cousin, Roger Catarino, played for the University of Tennessee at Chattanooga years ago. In one of his seasons as a starter (according to my admittedly spotty memory), they finished the regular season 10-1 (and #3 in Division 1-AA), beating UT in the process and losing to Ole Miss by a single point.
He was drafted by the Bengals (and the Cowboys, I think, during that brief period when the AFL and NFL were rivals and conducting rival drafts), and eventually ended up in Dallas for a brief training camp stint. Though he impressed them, a knee injury and his height (he's 5' 10") conspired to derail a nascent pro career. It didn't help that another guy named Roger had just finished his Navy commitment around that time.