Open the App Store and look in your "Purchased apps", it should be listed there. You don't have to back up your apps, all apps that you install are tied to your Apple ID account.
Open the App Store app, tap the bottom right icon (Updates). In the Updates screen, tap the "Purchased" button at the top and then tap the "Not on This iPhone" button at the top of the next screen. You will then see a list of apps that you have previously installed but are not currently installed. The app you seek should be in that list.