First, let’s attempt resolving this issue with your Apple device by trying a hard reset, then proceed from there if that does not resolve the problem:
Disconnect the device from it's cord, if plugged in.
iPhone 7: press and hold the power button and the volume down button simultaneously for about 10 seconds, or until you see an Apple logo.
iPhone 6S and older: Press and hold your Sleep/Wake button (on the top right) and Home button (on the front) simultaneously for about 10 seconds, or until you see an Apple logo.
When the Apple logo appears, release both buttons.
The next thing you should see after the Apple logo is the Setup Assistant a few minutes later.
If the above does not work, try connecting to a wifi network before activating.
If that still does not work, you may need to activate through iTunes.
Make sure you have downloaded and installed the latest version of iTunes on your computer before attempting this:
(Mac users can run System Preferences > Software Update (or “Apple Store” for OS X 10.9 users) > Check now to get the latest version for their system in most cases.)
Restart the iPhone. Make you default choices as usual but when prompted, choose "Connect to iTunes"
Then plug your iPhone into a USB port on your computer.
iTunes has an activation mechanism built into it that can reach Apple’s activation servers directly via the computer's internet connection.