First, specify if they are merely a Psychopath or a true Sociopath
Psychopathy is a generic term that means prone to aggression. Sociopath is what is generally used to describe when a person does not have emotions as we know them.
Either condition should probably restrict your player to Chaotic alignment (if you use alignments seriously, I know many sideline it) and possibly Evil or Neutral with Evil tendencies.
You could work together to homebrew some Traits and/or a Drawback to bring the effect into play. Does being a Psycho make it easier to Bluff and Intimidate? It probably makes Diplomacy harder.
If they want to be a Sociopath,
make sure that you talk out how far they are willing to let their character go. Are they trying to overcome their situation (ala Dexter) or are they looking to be the insidious bad-guy that's within the party? If the Paladin (or such) finds out, are you both willing to go into PvP? Or else, when they 'turn to the dark side' would they hand the character over to you, the DM and they pull out a backup?
A sociopath would technically be immune to [Emotion] effects. They simply don't have the capacity to feel like that. A psychopath wouldn't necessarily need this boon. In play I may homerule a Feat and require them to take it first level. That's a pretty powerful effect.
It's unlikely to affect your character in combat outside of that because everyone is a little psycho in combat out of necessity.
As far as rules, there is the new Moral Insanity Madness and this 3.5 Trait that you would have to modify to work with Pathfinder anyway.
Finally, here are a couple discussion articles on it to peruse.
/r/Psychopaths in Roleplaying Games
Giant in the Playground: Roleplaying a sociopath
The general concensus is that it will be difficult because they will, in order to read as their character idea, need to be 'a big deal'. They will by necessity make many situations harder. This could be good or a drag, depending on your group. As one of the posts to the reddit I linked points out, characters like "Monk, Holmes, House..." are the main character of their little world because of this.