should I use a 12 AWG wires?
No
Would normal wires be enough to hold on the current consumption if I were to connect it from a 24v dc power supply to a voltage regulator?
The current a wire takes is nothing to do with the voltage on the wire it is all to do with the resistance of the load.
If you are going to a voltage regulator then the current is unlikely to be greater than 2A so "normal" wire will do.