As mentioned in comments, staring at your opponent might off-balance some of them, just as behaving abnormally in anyway — constantly replacing pieces, or smiling as if there was a reason comes to mind.
As I mention elsewhere, you can try the long-shot trick of not pressing your clock to distract them. Probably not achieving much though.
Obviously nothing of that belongs to fair play, but I guess that's not much of this question's issue.
What actually happened to me in the last game of a 15-minutes tournament, as I had not much time remaining¹ was my opponent² — in an obviously losing position — play very fast, misplacing many pieces on the way, and, as I played my move and replaced some pieces on their squares, play his, and pretend I had touched the piece I was replacing, therefore had to play it³.
As I made the move I wanted, he would move the piece back and press his clock again, repeatedly, muttering some foreign words⁴ about “having to play”. In the end, he would keep his finger pressed on the mechanical clock, preventing me from stopping it. I lost most of my time to all of that, and wouldn't have had enough to mate would he have played till the end after the referee finally came and let me play the bishop. Hopefully, he just went self-righteous against the referee, so I won by “that”.
Not very psychological, will definitely get you a bad reputation, and unlikely to achieve anything in major events, but definitely throws-off your opponent, probably also for the next game. Rank pressure helps, especially after a tense game, etc.
¹ Like 4 minutes : well enough to win the endgame-with-a-bishop-advantage the combination we where playing lead to, but not enough to deal with nasty clock tricks.
² Ranked ~150 better than I did, he was playing for a prize, I was playing for 4th place and to enhance a friend's prize.
³ Hence faking a trebuchet zugzwang where I was about to move the said bishop.
⁴ It sounded like engrish, but in a French town that'll definitely catch off-guards your usual chess player.