In iOS 8 (September 2014) Apple allowed developers to create custom keyboard arrangements. In January 2015 two new keyboard layouts for iOS appeared for Esperanto users. They can be used in any application and iOS autocorrect does not mangle words while typing.
Viacheslav Shklyaev created a keyboard for Esperanto. It is called Esperanta Klavaro and is free. Information about the keyboard app is available at slava-sh.github.io/klavaro/ This app requires iOS 8.1 or later. The direct App Store link ishttps://itunes.apple.com/us/app/esperanta-klavaro/id957192189?mt=8&uo=4
The company Ludisto published its layout called Esperanto-Klavaro. Originally they charged 5 USD for it, but later made it free. It was available via their website http://ludisto.com/app/esperanto-klavaro/ which linked to Apple’s AppStore. This iPhone keyboard requires at least iOS 8.
In November 2015 Ludisto advised us that they have withdrawn their app from the Appstore because the app by Viacheslav Shklyaev is better.
Ĝusta Klavaro (obsolete)
This is an earlier attempt to provide an Esperanto keyboard arrangement for iOS. It is less convenient because the user has to type the text, copy it, and paste it into where it is needed. The Ĝusta Klavaro app can be downloaded from the Apple App Store.