Final answer:
The superior rectus muscle is innervated by the oculomotor nerve (CN III), which controls most extraocular muscles and is essential for coordinated eye movements.
Step-by-step explanation:
The cranial nerve that innervates the superior rectus muscle is the oculomotor nerve, which is also known as CN III. This nerve is responsible for controlling most of the extraocular muscles, which are the muscles that move the eyeball, as well as the levator palpebrae superioris, which is the muscle that lifts the upper eyelid. The oculomotor nerve originates from the oculomotor nucleus in the midbrain and plays a crucial role in coordinating eye movements.