yes , you can install youtube but it is not original youtube from google but you can use youtube alternative for iphone 4 by jonas gesnner its called protube .
for installing protube;
1)you need jailbroken iphone 4 .
2)open cydia sources , click on edit , add ,copy paste following repo;
REPO: http://cydia.kiiimo.org/
3)after adding repo click on search and find protube and install it .
4)after installing you can find protube in home screen on your iphone .
5)launch protube you can now use youtube in your iphone 4 .
6)enjoy!!!