Sorry, but you can’t turn off your IP address. Even if you were able to do so, you wouldn’t be able to use the Internet. When you go to a website, your browser sends along your IP address. The server then knows where to send the page that you requested. The same is true for apps like BitTorrent; people running BitTorrent can’t send you data unless they know your address.
However, all is not lost. Imagine that you have a house with no address, but you still want to receive mail. You could rent a box at the Post Office and then give out that address. On the Internet, you can do the same thing with a Virtual Private Network (VPN) such as IPVanish.
Further reading: Tips to Avoid IP-Address Tracking.