7th stat: Psi
Psi = Avg of Int, Wis, Cha
3-10 = No Psionic Potential. 50% chance of immunity to mental psionics.
11-12 = 0. May only use psi powers with some sort of psi-boosting aid (item, spell, eardwelling parasite, etc.)
16-17 = +2
18 = +3
Roll 1d5 during character creation. this is the character's Psilignment (passive defense. map to the cards if you wish)
Psionic attack: roll 1d5 per point of Psi bonus. An opponent who is aware rolls 1d5 as well. If the opponent's number is rolled on any of the attacker's dice you hit. Use the opponent's Psilignment if the opponent is not actively expecting the psi power.
(variant for high psionics and extra headplosions: Roll 1d5 with an additional 1d5 per point of psi bonus. in this case even those with no Psi bonus can use powers unaided.)
(Variant for those with those wacky cards: have the attacker guess the opponent's card. This makes it much easier to hit a Psilignment once the attacker figures it out, assuming the person doesn't automatically start defending themselves.)
Powers: Pull powers from whatever source you want for your game. D&D, some other game system, whatever. Maybe even give each psilignment something special.