On paper, it can be done with some heavy modification. The wireless card would need two create two independent connections (one from the router to the pc, and a second from the pc to the next device). Since 99% of cards do not do that out of the box (and I am not certain any can be made to do that), I don't think it's possible.
I promise you it is much easier to buy a wireless ap/bridge for around $50-100 US. I have the D-Link DAP-1522 and it works like a beastly charm as both a repeater or a bridge. I currently use it in bridge mode for my Sony BD player and DiSH Network HD box (to pull guide info faster, etc). I can manage its settings via its ip (mine is 192.168.0.50).