Im no ee so take everything I say with a grain of salt. I just read here and there and try and pickup stuff.
Your circuit would need that variable resistor set to aprox 1050ohm to make 12v, check that.
Youve also got a 10uF cap in there, I assume your doing this to reduce ripple ? something you really shouldnt need for a 12v fan. never the less, you dont have a protection diode between adj and Vout like the datasheet recommends to prevent the LM317 from being damaged by that cap discharging through the adj pin. Id pull that cap for now just to test. Do you have another LM317 you could test incase that one your using is toast ?