You can back-up your game save to the cloud if you are playing using either iOS Game Center or Android Google Play.
You can view the Settings menu in-game to confirm that you are logged into Game Center or Google Play. If you are logged in, you will see an “Unlink Game Center” or “Unlink Google Play” button at the bottom of this menu.
If you log into another device with the same Game Center or Google Play account, you will be able to retrieve your save. When you start the game on that device, it will automatically recognize your Game Center or Google Play account and will retrieve your save.