If you are not the party that does the parting (the victim of a no fault divorce) but:
I Corinthians 7 “[12] But to the rest speak I, not the Lord: If any brother hath a wife that believeth not, and she be pleased to dwell with him, let him not put her away. [13] And the woman which hath an husband that believeth not, and if he be pleased to dwell with her, let her not leave him. [14] For the unbelieving husband is sanctified by the wife, and the unbelieving wife is sanctified by the husband: else were your children unclean; but now are they holy. [15] “But if the unbelieving depart, let him depart. A brother or a sister is not under bondage in such cases: but God hath called us to peace.”
That obviously covers those with whom neither were Christians before being married, but then one became Christian.
When you aren’t one of God’s children, it would appear you can’t vow to God.