Binance for iOS
Binance has developed an app that works with the iOS, though it is still in beta stage, currently (on June 26, 2019), at 1.6.0 version.
Their iOS desktop app is available for download on their official site (here is the link: https://www.binance.com/clientDownloads.html). This app is intended for MacBooks, iMacs, and iPads.
There have been some issues with the iPhone app, as such it is no longer available on iStore. Furthermore, it is currently also not available on Binance website. Some iPhone users have been able to download a desktop app and use it on their iPhones successfully.
No matter which system you are using, there is always an option of logging in on their website that way you can access your account on any iOS device.