I recently wrote a research paper and want to submit it to a journal but as I wrote it on my own and it's my first paper, I would like someone (a faculty member or a PhD student) to review my paper and in exchange I offer them an authorship. How do I approach faculty members and have them do so?
I think it is pretty hard to make a blind contact and get any positive response. I suggest that your first step should be to contact a professor at your university for advice. Perhaps they are willing to do it themselves, since they have some relationship with you. But you can also ask them for advice as to who might be a good person to do it. If you don't want it done locally, say that you are looking for outside advice. Professors normally have a wide circle of contacts.
The best thing is for such a professor to make the request on your behalf rather than having you make it directly. It is harder to turn down a request from a colleague than from an unknown student.
But don't offer "authorship" for a review. Many people (most?) consider that improper. Authorship should only come if the project is not yet complete and you are seeking collaboration on finishing. If the request comes from another professor it shouldn't be expected in any case. It is just a favor that academics do for one another.