Connect my IPhone to my fax machine?

Unfortunately you cannot tether in that way...if the fax uses wireless, and your cellular service provider supports Personal HotSpot, you can create a personal hotspot with the iPhone and then join that network with the fax if you can control the fax in that way, and use the iPhone connection to cellular data network of your provider.

There is no way to hard-wire them togther, however.

There are several web-based fax services that may meet your needs.

Some are free for limited use, most are inexpensive.

Google should be able to provide you some direction.

No, there isn't a connector like that. And iOS is not deisgned to support that kind of activity. You could send material to a computer conneced to the fax if that would serve your needs.