Could flight control be achieved by rotating a wing entirely?
Yes, it has been tried before and is regularly used on many horizontal and even some vertical tails.

However, in subsonic flight an elevator will offer better efficiency. Only in supersonic designs is the full-flying tail the clearly preferred option.

To move the whole wing needs very strong hinges and actuators, but there were some which did even this:


Mignet HM 14 Pou du Ciel (picture source). It was light and flew slowly enough that moving the whole wing was not an issue.





The Vought F-8 "Crusader" and XF8U-3 "Corsair III" could jack their wings seven degrees up in order to improve fuselage attitude and pilot visibility during take-off and landing (picture source).




Even all-moving outer wings have been tried for roll control, albeit in only very few aircraft. Three I know of (and all of them were built once only) are:


Granger Archaeopteryx,
Short SB.1 glider, and 
Short SB.4 Sherpa, the rotated wingtip of which is shown below (picture source).