A friend of mine is one of the best leaders I know. He's also deeply introverted. Anyone meeting him for the first time could easily think he's a back office guy - and the one at the very back, maybe in charge of the old metal cabinets storing the paper archives.
Au contraire. He's the guy who transformed an ailing world class IT company so that it is now turning over several billion dollars per year. So how? His twin essential gifts are his ability to listen and also recognize the value in ideas that are not his own. Corollary to this is the near adoration of his staff because he is fair and always rewards those good ideas.
Recently I dropped by his company's hospitality booth at a trade fair. When seen among his team, he was so obviously the guy in charge although very quietly. As we sat having coffee, it seemed that everyone wanted to give him news, information, their opinion or just grin at him and say hello. Throughout he was solemn as an owl, but when he looked at his colleagues, he seemed really to see them. He made gentle jokes and poked mild fun at the pretence all around his company's tent.
Leadership is often associated with personality-plus sorts of people in constant interaction with the world around them. They create a focus point, make things happen, draw others together - all excellent features of leadership. However they often need to learn to listen. Introverts, in contrast, bring stillness to an interaction, but need to express themselves effectively to avoid leaving people guessing about what they mean.
For sure, both introverts and extroverts can be leaders - although the interactions they have with their teams will look very different. The challenge is balance - both listening with speaking in a skilful way to ensure communication works well.