http://www.gottabemobile.com/2012/09/19/how-to-get-youtube-back-on-ios-6/
After upgrading to iOS 6, users may notice the YouTube app is missing from their home screen.
In addition to ditching Google Maps for the new Apple Maps app, Apple pulled the YouTube app from iOS 6, but users can download a new and improved YouTube iPhone app from the App Store. -gottabemobile.com
This link will show you how.