iPhoneism has provided several methods to fix this problem as well as a recommendation to wait the problem out if these fixes don`t work for it would probably be an issue with Apple`s activation Servers:
Method 1: Do a clean install of iOS 5 on your iPhone 4S.
Step 1: Download iOS 5 firmware IPSW for iPhone.
Step 2: Connect your iPhone 4S to computer and launch iTunes 10.5.
Step 3: Put your iPhone 4S in DFU mode.
- Press and hold Power key for 3 seconds
- Press and hold both Power and Home keys for 10 seconds
- Release Power key but keep holding Home key until iTunes prompts you that an iPhone has been detected in recovery mode
Once iTunes prompts you, press and hold the Shift key on Windows or the alt key on Mac and click on Restore. Select the iOS 5 firmware IPSW for iPhone 4S that you previously downloaded and click on OK. iTunes will now begin a clean install of iOS 5 on your iPhone 4S.
Step 4: After the installation finishes, don’t restore your device from a backup. Set it up as a new device and then try activating FaceTime. It should work. You may restore your device from the backup afterwards.
This method has particularly proved to be helpful for those who face this error on iPhone 4. It also proved to be helpful for iPhone 4S owners as well.
Step 1: Launch Settings.app.
Step 2: Go to General followed by Reset.
Step 3: Tap on Erase All Content and Settings.
All content and network settings on your iPhone 4 or iPhone 4S will automatically be erased and your device will reboot. The key here is to not restore your iPhone using a backup. If you opt for this method, do keep in mind that you will have to install all apps and data manually after all content and settings have been erased.
Method 3: Manually tweaking the Settings.
Step 1: Turn FaceTime off from the Settings.app
Step 2: Add your telephone number to your contact list. Add your number in iPhone, not mobile.
Step 3: Go to Settings>Mail, Contacts, Calendar>My Info and change My Info by selecting the contact you created.
Step 4: Make sure your number is being reflected in My Number. Check that by going to Settings>Phone. Turn on Show My Caller ID and International Assist.
Step 5: Go to Settings>Store and login using your Apple ID.
Step 6: Once done, hard reset your iPhone by holding Power and Home button until Apple Logo appears.
Step 7: Connect to WiFi after your iPhone boots up.
Step 8: Now turn on FaceTime and activate by logging in with your Apple ID. After a few seconds, you will be able to use FaceTime.
