I agree with Simon; the swearing an oath is interesting, but shouldn't replace opening your mind.
In the original fiction, Conan's philosophy is that the gods don't really care that much about us. In the original film, he tells Crom to go to hell if he won't help him, and doesn't expect anything to come of this. Given this, I'd frame the move along the lines of impressing the gods.
Get the Gods' Attention
When in a charged situation, swear an oath to your god, then roll +Wyrd. On a hit, your oath comes to pass. On a 10+, you have impressed your god and gained their favor, in the form of +1 forward. The gods are capricious, and keeping their fleeting attention is like trying to hold sand. On a miss, your opponents have impressed their god instead. Woe unto you.
I can see Conan doing that, for sure. :D
As for opening your mind, the real weirdness in Conan was almost always sorcery. I'd say keep the move, but frame it within the fiction that way. Of course, Barbarians hated sorcery, so maybe make it either involuntary on the character's part, but still the player's choice. Or maybe for Barbarians, frame it so they're listening to their instincts or the voices of their ancestors.