Rome: Total War lands on iPhone on August 23
Moreover, your progress will carry on if you transfer your save file from the iPad on the iPhone. Bear in mind though that not all iPhones are compatible with Rome: Total War, but most of them should allow you to play the game: iPhone 8 plus, iPhone 7 plus, iPhone 6s plus, iPhone 6 plus, iPhone X, iPhone 8, iPhone 7, iPhone 6, iPhone 6s, iPhone SE, and iPhone 5s.
If you haven't played the iPad version yet, you should know that Rome: Total War for iPhone offers the full experience, with a suite of features tailored specifically for phone, such as a redesigned user interface and enhanced touch controls.
In addition, Feral Interactive announced that Rome: Total War will use the latest version of Apple's Metal API, which should provide improved performance, enhanced graphics, and reduced battery usage.
Besides having one of the supported iPhone models, you should also reserve at least 4GB of free space to install Rome: Total War. For more details about the game, check out the game's page on App Store.
source: Feral Interactive, App Store