Theoretically, on a Mac, you could just open the project in Xcode and build it there.
Practically I had no luck so far with this, a bunch of signing errors pop-up…
Update: I made it work!
After you open your game in Xcode, you will still need to get a signing ID and a Provisioning Profile. Go to Preferences → Accounts, log in and hit Create on “iOS Development” under Signing Identities.
Download both the ID and the Profile (or check where they are, since it may get downloaded automatically) and go back to UE4, go to Edit → Project Settings… and from them to Platforms → iOS.
There on the second box it says “Provisioning” if it doesn’t find them automatically, then go to each "Import " Button
and find them.
If all went well, the ID and Profile will turn green. Then click the little arrow next to the “Launch” button and select your device. Hit Launch and after a few seconds, voila! It’s on your iPhone!
After that you will still need to go to your iPhone’s Settings and “Trust” your Developer Account (Settings → General → Profile → Your Developer Email)
Obviously you will still need an Apple Developer account, but you don’t have to sign in for the Developer Program.