There is an issue with the first boot of the game not receiving data from the iCloud, to fix it simply close the game by pressing the HOME button (located at the bottom of the device) and select Carmageddon again. Your iCloud save data should now be there! (Make sure you are signed into the same Game Center profile aswell!)
In addition make sure that the 'Documents & Data' setting for your iCloud account is turned on, otherwise the save game for Carmageddon will not get synced to the iCloud. To check this setting, do the following: Go to 'Settings' for your device. Select iCloud and scroll through the list to find 'Documents & Settings'. If it’s off, turn it on and voila your Carmageddon save game data will now get synced to the iCloud.