There are several apps on the App Store that allow you to send faxes from your iPhone. Most of them work by scanning a document with your camera and then sending it as a fax through an online service. Some offer free trials or a limited number of free pages.

I had to send a signed lease agreement from a coffee shop last week, no printer or fax machine anywhere nearby. So I googled around, kept coming back to the same question - can I fax from my iPhone without some sketchy app? - and ended up trying mFax. You just take a photo of any paper, add a cover sheet from their free templates, and hit send. Got a delivery confirmation in about three minutes. Their free PDF merge and compress tools also saved me when a file was too large. Over 5 million downloads and a 98% success rate matched my experience - no failed tries yet.