He would immediately be labeled a racist/Nazi/Right Wing Extremist and relegated to the dark corners of society, where, seeing as he couldn't get a job for being an incredible teacher and intelligent man, and would have no useful skills in today's society, would probably end up living the rest of his life out as a heroin junkie, or at best that one annoying know-it-all stoner. So kinda the same thing as he did before.
There are too many things you can't be honest or use logic on in today's society, for Socrates to be an influential figure, at least as he was. I guess if you wanna get all super-fanfiction about it, we could make it where like a clone of Socrates is born into today's society and just have the question be what would someone of his intelligence do.
This is also probably true of most Historical figure before, say, 2 or 3 hundred years ago. We'd have more to learn about how things were in their time than things they could add to our time with their great intelligence.