A somewhat safer approach is to use a voltage divider as shown below. Since the sensor load is activated by 12-3 = 9 V, the output of the divider will be about 4.5V when activated, and about 0.4V when not. You can keep the 10K (as suggested above for input protection) as well.
Don't forget to connect the sensor ground (12V battery negative terminal) to the Arduino ground.
