Let's say I have a PDF on my computer with information relating to my question that I cannot find elsewhere on the Internet.
Is it possible to link the PDF to a question or an answer I post on one of the Stack Exchange. network posts?
No. Questions are expected to contain all the relevant information, and can link to other resources (like additional background) on the web. The same issue arises with log files on Stack Overflow; you can't attach those either.
Try to distill out the important information from the PDF and include it in the question. If you need to refer to a longer document, you'll need to find a place to host it. If your question involves the formatting of the PDF (like you're trying to figure out why something came out the way it did), a screen shot might suffice.