Etymology - which came first, "oath" or "swear", as applied to cursing?

These two words seem related; they are both related to the double meaning of “to affirm” and “to curse”. Are they related, and if so, which came first?

“To swear an oath” dates back to 472 A.D. (OED). The meaning, “to curse,” dates from 1225. Very old, but not old enough.

It also shows up (at least) in translations of earlier works:

The Argonautica, book four ~ 200 BC.