From Samuel Martin's Reference Grammar of Japanese (1975), p.191:
The intransitive verb 向く【むく】 means 'faces, fronts on' or 'is suitable for, suits' with N に; but with N を it is a quasi-intransitive verb of motion meaning 'turn (one's face) toward)' [...]
He gives these examples:
横【よこ】を向いて【むいて】 turn to the side
前【まえ】を向いて【むいて】 turn to the front
This verb belongs to a class of verbs of motion which take を-arguments, which we nonetheless might want to consider intransitive. Martin uses the term "quasi-intransitive" to describe this sort of verb. You're probably familiar with examples like:
公園【こうえん】を散歩【さんぽ】する take a walk in a park
橋【はし】を渡る【わたる】 cross a bridge
家【いえ】を出る【でる】 leave home
All of these are subtly different, and none is exactly like 向く, but I think that we can treat all four as examples of Martin's "quasi-intransitive verbs of motion".
If you consult monolingual dictionaries, you'll find that they disagree with one another on how to classify this use. For example, 明鏡国語辞典 calls 向く a transitive verb and treats the directional object as though it's a normal object. But other dictionaries like 広辞苑 call the verb intransitive.
You can find some previous answers discussing this use of を and the question of whether these verbs should be considered transitive if you search Japanese.SE. You can also find a description of some of these uses of を in A Dictionary of Basic Japanese Grammar by Makino and Tsutsui starting on page 349, though it doesn't cover 向く specifically.
I'm afraid this is one of the sticky points of Japanese grammar where descriptions differ, but hopefully you can look at how the verb is used and make sense of it one way or another :-)