Tony is an extrovert by nature.
I would say he's very, very much an introvert -- specifically an outgoing introvert. He puts on a big show of being open and gregarious, but it's all just a facade he uses to distance himself from other people and avoid any real intimacy. Mostly, his intellectual and emotional life is inner-directed, not outer-directed. The place where he's most at ease is in his lab, alone, exploring what his own mind can create, with only his robot friends for company. He resists sharing his plans and projects with other people. And his superpower is literally hiding himself inside ever more elaborate suits of armor. It doesn't get more introverted than that.