Relays don't need resistance - they just need a proper coil driver. Simple NPN transistor will do. The little 20mA MOSFETs that make up an Arduino output aren't strong enough to support a relay coil. But they can drive a transistor, which can drive a coil.
See attached. The 1N4001 diode dissipates current in the coil when the transistor goes from On to Off.
The LED and resistor is there so you can see when the coil is energized, you can leave that part out.
The Resistor between the Arduino and the NPN base keeps the Arduino from trying to drive too much current out; the base acts like a diode to ground when the Arduino output goes high, having a ~0.7V short on a high output is bad for the Arduino.
