Final answer:
The inferior oblique muscle is innervated by the CN III (oculomotor) nerve.
Step-by-step explanation:
The cranial nerve that innervates the inferior oblique muscle is CN III (oculomotor).
The oculomotor nerve is responsible for controlling most of the eye's movements, including the superior, inferior, and medial rectus muscles as well as the inferior oblique muscle, which allows the eye to look up and rotate.
This nerve also controls the levator palpebrae superioris, which lifts the eyelid.