It will work fine on 12V.
You do not have to split it, just supply 12V to the power connector on the Arduino board, it will take what it needs.
The only problems you may have are if the motor takes such a big current that the voltage drops too low to supply the Arduino. This would cause the Arduino to black out and reset momentarily.
You can guard against this by Giving the Arduino its own reservoir of charge in the form of a large electrolytic capacitor (say 4700uF 16V) and a diode so the motor doesn't steal it.
|--------------- to motor
-------|>|--------- to Arduino
|
12V =
|
--------------------------