Bible says 'let your yes be yes and your no be no' and not to swear such oaths to begin with. its a pretty common thing anymore, to speak like that. "i swear on a stack of bibles i didn't eat all the cookies". Or the courts swearing people in on a bible, which is ironic since the bible says not to. But oaths are pretty binding.
But really, i'm not understanding the question fully. Swear an oath to God and ask forgiveness? Forgiveness for what? And what oath are you swearing to? Need to clarify.