watch youtube on ios 6

Can I install YouTube App in iOS 6 iPhone 5, iPad, iPod touch?

The issue Users of Apple iOS 6 were disappointed to find that the YouTube app is no longer pre-installed on there devices (iPhone 5, iPad 4, iPhone 4S, iPhone 4, iPhone 3GS, iPod touch 5, iPad 3, iPad 2). How comes this peculiar issue and how to fix it?