Two thirds of your arm consists of your triceps. So it's important to train your triceps and biceps for bigger arms.
For biceps try different pull up variations (overhand grip, underhand grip, mixed grip, rope pull ups). One of the best bicep exercises is pulling rope. Just attach a rope to a heavy object that you can pull towards you.
For triceps try different push up variations (close grip, wide grip, neutral grip, decline). For increased resistance do push ups with blast straps. Blast straps can easily be made at home. Dips are also a very good exercise for the triceps.
For increased resistance during pull ups and dips, attach a weighted object on your body with a rope.