Yes, Like Lefty Said.. 12V will work.
But (There MIGHT be a But) there might be problems with noise and transient voltage spikes if you are running DC motors and stuff.
So, I would vote for using a voltage regulator and putting out about 8 or 9 volts to the Arduino Pwr In.
And, for more confidence, I'd think about more insurance against funny voltages that may be out to get you and your Arduino:
- Have some good big common ground point on the car chassis where the motor/ controller negative and the battery negative come together. Run a separate wire from that to Arduino GND.
- Have a couple of good Bypass Capacitors right at the +12 side of your voltage regulator. Say both 1000 Microfarad 20V electrolytic and .1 uf disc.
- Have a MOV (Metal Oxide Varistor) rated at 25 volts or less connected from the +12V supply at your arduino area, to the Arduino GND.
You circuit is not going to draw much current at 8 or 9 volts. Figure it out. Think about a small value series resistor between the vehicle +12 and the input to your regulator. This makes your bypass capacitors much more effective. If you are going to draw 1/2 amp (500ma) then a 1 ohm resistor will only drop .5 volts, but will improve the "filtering" of the bypass capacitors a lot.
I've fought these things on cars and boats, and become probably over-pessimistic about vehicle raw battery connections
But do what you can, and if you have a once-in-a-while crash or misfunction with your Arduino, look at the Purity of DC...