Arduino will supply 5V and max rated pin curren s 40ma. You will need an external 12V power supply to manage this. Also, don't connect the 12V supply to ANY of the Arduino pins. You can use a 12V PSU to power the Arduino though.
With the right mosfet and a connection to the right point on the power supply somewhere before the regulator on the UNO (assuming that can manage 12 volts an current to spare), it should work.