Is "divine" acceptable as a verb?

Yes. The usage of divine as a verb to mean 'to discover' or 'intuit' or even, yes 'practice divination' is perfectly acceptable and useful and should be found in most better dictionaries.

However, it is less common than the religious, noun definition, so you'll need to skip past a number of unrelated uses. For instance, Merriam Websters has it listed last of three.