Unclear, but I'd say No, the Centaur cannot turn itself
The Oath of the Ancients paladin's class feature you are referring to is this one (PHB, pg. 87):
Turn the Faithless. You can use your Channel Divinity to utter ancient words that are painful for fey and fiends to hear. As an action, you present your holy symbol, and each fey or fiend within 30 feet of you that can hear you must make a Wisdom saving throw. On a failed save, the creature is turned for 1 minute or until it takes damage.
Yes, you are a fey creature, and yes, you are within 30 feet of yourself. However, it continues to say:
A turned creature must spend its turns trying to move as far away from you as it can, and it can't willingly move to a space within 30 feet of you. [...] If there's nowhere to move, the creature can use the Dodge action.
So whether this makes any sort of sense is ultimately up to the DM. Since a creature cannot get away from itself, does that mean it simply doesn't affect itself (which is what I would rule) or that it has to repeatedly take the Dodge action until it is no longer turned (the only other ruling that I can think of that would make any sense)?
Given that the feature is called "Turn the Faithless", this implies that if you are a paladin, then your faith (at least your faith in your own oath) means you cannot be faithless, so therefore it cannot affect you, although this is my interpretation of the name of the feature rather than any rules. Still I would say that it doesn't make any sense for you to be able to turn yourself, but again, that's just my preferred ruling.