It sounds like the bearing on the fan has gone bad.
You can try and get an aftermaket cooler solution to fix it. You can also try to get a RMA for video card, but I doubt that it will work since your card's warranty probably expired at this point. The last thing you can try is take apart fan bearing assembly and put in some lucubration to see if it helps.
Ivy Bridge i5-3750K@stock, Gigabyte Z77X-UD3H, 2x4GiB of PC-12800, EVGA 660Ti, Corsair CX-600 and Fractal Refined R4 (W). Kentsfield Q6600@3Ghz, HD 4850 2x2GiB PC2-6400 = 4GiB total, Gigabyte EP45-DS4P, PC P&C Silencer 610W, and PC-7B.