Is it possible to receive a fax on my iPhone?

Another option is to ask the sender if they will scan and send as an email attachment instead of faxing. I've yet to find (although I'm sure they exist) a company or government agency that wouldn't do that when asked.

Not from a fax machine. However there are some email fax services that allow you to fax to them and then can covert and send it to an email account. You would have to search for that.

Search the App Store for "Fax".

You may find an app that suits your needs. eFax looks like a strong contender.

(I have no financial interest in eFax.)