How to quote a draft in my thesis?
If it has been published, ask the author for a pdf of the published version (from your question I got the feeling that the paper has been published). This would also be easier to share with your supervisor later on. It makes no sense to cite or quote a draft version if the paper has been published. At least ask if the draft has identical content as the published version. If so, you could maybe get away with using the draft but citing the published version in your reference list (not ideal though).

Otherwise, cite it as a working paper/draft, by including author, title, and the date when you recieved the paper, see e.g. Chicago manual of style online or MLA style guide.