Using 12 ga wire to pigtail a receptacle
The 12ga wire is perfectly fine to use as a pigtail for a 15amp circuit.  

Just note, The pigtail needs to be securely bound to the existing wiring.  So a couple of twisted wires and electric tape is not enough, wire caps or something similar needs to be used.  And if the existing wiring is aluminum, you will need to use specialized caps to bind copper wire to it.