It had to have happened in the 90s, but I can't remember either the tournament or Karpov's opponent (probably some Spanish tournament, like Linares or Dos Hermanas). Karpov was upset with the organization for some reason, and he complained by playing 1. e4 and offered a draw that was accepted by his rival. As Karpov would say: "What would he do? Play for a win?"
I've tried some simple Googling via "shortest karpov game" and similar stuff, but I've gotte nothing at all. I have no idea how to use databases for a search like this, but I suspect that-for obvious reasons-this game probably isn't in any of them.