It can occasionally be said, but most often per means "to", e.g. "Mi pagano per premere un pulsante" (they pay me to press a button), or to express a subdivision: "Pago per loro" (I pay for them, meaning I pay for their purchase), "Pago per le patatine fritte" (I pay for the fries, meaning someone else will pay for other expenses).
So this is true with any direct object of "pagare"? Is it correct to think of "pagare" as meaning "to pay for"?
On a utilitarian level, I mean. I realize that "to pay for <something>" uses an indirect object for the verb, while "pagare <qualcosa>" uses a direct object. But my question isn't strictly grammatical, it's usage. After years of speaking Italian (not very well), I had never understood that "pagare" takes a direct object instead of "per" and an indirect object. If this is the normal usage, then I really want to incorporate that into my speech.
Incidentally, this sort of thing is why I have been finding Duolingo so useful. It has been great for helping to fill in the (many) cracks in my understanding of how Italian is spoken and written.