What is the verb form of "conjunction" in the logical sense?

Logically speaking, the verb conjoin really should be acceptable. A conjunction is the act or product of conjoining. It's the same stem, so if one form is deemed sufficiently precise to refer to the operation, why shouldn't the other be? The counterpart, for "or-ing", would be disjoin. Conjunction has a more specific meaning in propositional logic than in general and grammatical usage. Under the logic that two statements could be "conjoined" with the OR operator, all disjunctions would also be conjunctions. That's obviously not a very useful sense in context.

To clarify to readers the fact that you're using the word in a context-specific way, the first time you use this verb, simply follow it with "(i.e. join with AND)" or "(as opposed to disjoin)". If you're going to use the verb that way repeatedly in a longer text, you might briefly but explicitly explain in a footnote instead. Given how infrequently we use conjoin in general language, I don't think this overloading of terminology would be likely to cause ongoing confusion. (It's not as if it will be mixed with uses of that verb in its everyday sense.)

Personally, I think "conjuncted" just sounds influent.

Why reinvent the wheel? The manual's target audience understands what an AND operation is, so it makes more sense to say "The values are ANDed together" than "A logical Boolean operation is performed on the values".