The NFL requires draft prospects to take the 12 minute Wonderlic IQ test. The average score is 21 (up from 20, perhaps due to the Flynn Effect), with each additional right answer the equivalent of 2 extra IQ points.
The New England Patriots' All-Galaxy quarterback Tom Brady (a record 50 touchdowns and only 8 interceptions in the regular season) got 33 right out of 50 for an IQ of 124 (about the 95th percentile). The Giants' younger Eli Manning, little brother of Brady nemesis Peyton Manning (for whom I've seen reports of 108 and 114), scored a 39 for a very high 136.
I'd still bet on Brady (if his foot is okay).
How often in American life do we see two competitors going head to head who average 130? We didn't in the last Presidential, where the average was probably around 120.
A couple of caveats: the Wonderlic is the quickest and dirtiest of the legitimate commercial IQ test, so there's a bigger margin of error. Players are allowed to take it more than once, so these rumored scores might not be their average, just their high scores. And with so much money riding on draft choices, I wouldn't be hugely shocked to find that now and then some player's agent had somehow gotten his hands on the questions ahead of time. (I recall one QB a few years ago who went from something like 88 to 132 when he took it again.)
I don't see a strong correlation between scores and performance for quarterbacks. But there's a substantial restriction of range problem: All NFL quarterbacks were previously college quarterbacks, so the players who were really bad at mastering a complicated playbook were already removed from the picture. I could believe that Dan Marino, who had maybe the greatest throwing motion ever, scored below 100 — he peaked in about his third season and didn't really adjust after that as the league adjusted to him.
Of course, a lot of what NFL quarterbacks need are cognitive skills that aren't tested well by traditional IQ tests. For example, what the Air Force calls "situational awareness" is very important in a dogfight — you can't concentrate too much on one thing or you'll get shot down by somebody you weren't paying attention to — and in a football game. High IQ people, such as mathematicians, can sometimes have too much focus on what they are concentrating upon to function well in daily life.