Arcimbaldo has hit the nail on the head there. You would need to find a way to increase the voltage to the fan, which if you wanted to use the PSU connectors would mean the next step would be to 15.3v.
Now, I am going to say this once. If you do attempt to hot wire your PSU to join the 12v and 3.3v lines to one source, all you will accomplish is to destroy your pc.
Why not just spend £3 on eBay and get a 1200rpm fan....