How can I use Tor browser on my iphone that is not jail broken?
Even after jailbreaking an iOS device, I'm unaware of any way to run Tor Browser on it.
However, you can approximate Tor Browser on Apple's iOS with the open source Onion Browser, by Mike Tigas. Onion Browser will use the Tor network for transport.
Onion Browser is not a Tor Project app. That said, it does appear to be developed and distributed with attention to the details of anonymity. See http://onionbrowser.com/ for more.
Further, Onion Browser is a minimal browser, and not a fairly full featured Firefox version like Tor Browser is. This might present you with a fingerprinting issue, depending on your threat model.
If you use it, do heed the additional warnings Onion Browser gives you about what it cannot anonymize due to the nature of iOS.
Source code: https://github.com/mtigas/iOS-OnionBrowser
There are several good TOR browsers for iOS. These are not supported or endorsed by the TOR organisation, but they include a copy of the open source TOR code with the iOS UIWebview component:
Safe Browser Secure is a free IOS/IPhone/IPad browser that has a very stable TOR implementation to allow you to browse normal web sites anonymously and access .onion sites. It also supports TOR bridges, and is the only iOS TOR browser to support pluggable transports (obfs2, obfs3 and ScrambleSuit), crucial if your government or ISP blocks TOR, like the Great Firewall of China. Disclaimer: marcelleh profits from selling this app.
A minimal web browser that encrypts and tunnels web traffic through the Tor onion router network and provides other tools to help browse the internet while maintaining privacy.
A full-fledged Tor-powered browser that offers you a REAL solution, with multiple tabs, customizable start screen, and much much more.