When someone is a psychopath they display easily discernible traits. Igo, in Shakespeare's Othello, displays a number of these traits, so it can be argued that he was, truly, a psycho path.
Some of those traits are a lack of compassion for others, cold heartedness, shallow emotions, viewing people as pawns, charm and guile, lack of guilt, and the ability and desire to actively manipulate those around them. Igo has done each of these. One great example is that of superficial charm; of pretending to be a friend when they are not.
Iago in Act III, Scene III pg. 106 shows his psychopathic tendencies when he drives Othello to suspect his wife. He says: “I humbly do beseech you of your pardon, For too much loving you”. This is a clear example of his pretending to be Othello's confidant and friend, but obviously the reader knows better.