Yes, there is! It is called CookShelf and you can download it from the Apple App Store or the Google Play Store. If you have an Eat Your Books Premium membership, the app is included and syncs your EYB Bookshelf across to the app. Just make sure you sign-in with the same email you use on EYB. The app has cool new features like a barcode scanner for adding your books.
If you prefer to use Eat Your Books on your smartphone, you can still do that. It will restructure the page to fit your phone screen. All the features of the full site can be used on a phone. You can learn here about adding an icon to your phone to make one click access to EYB easier. See more about using the mobile version.