Nouns readily convert into verbs in English. You will certainly hear parent used as a verb. It's redundant in my view, given that we have the perfectly good verbs rear and raise, but those who prefer to parent their kids never bother to ask me about usage. It's vexing. :-(
It does if used in the present continuous ("We are parenting ...") but I must admit the first thing that came to my mind was "Helicopter parenting" (a noun).