User blog comment:LostInRiverview/Monthly Question - June 2014/@comment-25027276-20140605151336/@comment-4568327-20140605163021

This was possible in The Sims 1, with The Sims Creator. You could take a portrait and stick it onto a Sim's face. Only problem was that making the eyes blink and the mouth move might be a challenge in the later games... well, The Sims 2, at least. It didn't matter in The Sims 1 because you hardly got to see much detail of your Sim's faces.