How would I anonymize my Android device and it's IP address? I don't want to be rooted as well, using a GS4.
You can use a VPN application, which usually works with no root access but approaches what you're looking for. In addition, you can use Hideman VPN. Also, one of your question tags are Tor. You can use Tor, but only the Orweb Browser will stay anoynmous. Without root, it's not your device that's anonymous.