Look at you, badass! Amazingly, says arm wrestling heavyweight world champion John Brzenk, "curling biceps has little to no value in arm wrestling." In fact, "arm wrestlers typically call it pulling, not curling."
But you do indeed need to bulk up. Brzenk advises using a pulldown cable machine with a grip handle and pulling down, then across the body.
As for technique:
1) Put your dominant foot forward to lean on.
2) Try to bend your opponent’s wrist away from yours.
3) As you push down, pull his hand toward you as if you were curling weight.