Can an introvert attact women?
Sure, why not. Any guy can attract women.
Look no further than Neil Strauss in 'The Game'. Introversion and extroversion are little more than examples of self-estimation and the behaviors that exemplify them. I'm an introvert and an extrovert. I'm a choleric, phlegmatic, pragmatic, cynic, sarcastic, opptomistic, realist and that's all before noon depending on what my personal condition are.
That's always been my belief: That "pure" introverts or extroverts are very rare. Most people at any given time are somewhere between the two extremes.
I was at a party a couple months ago where some lady had memorized this quiz that's supposed to pin you to either extreme, and she was getting really frustrated with me. She never got past the first question:
Her: Can I give you a little quiz?
Me: Sure, ask away...
Her: When the phone rings, do you look forward to answering it?
Me: It depends on who's calling me.
Her: What if you don't know who's calling?
Me: That's the glory of caller ID. I always know.
Her: But what if they have caller ID blocked?
Me: Then I let it go to voicemail.
Her: Hah! That makes you an introvert.
Me: Because I want to know who wants to talk to me?
Her: Because extroverts always look forward to talking to someone.
Me: And it's important to you that everyone here fits neatly into one category or another?
Her: It's important because <guy she's seeing> claims to be an extrovert, but he might really be an introvert.
Me: Mmmkay, so why are you obsessed with giving everyone else this quiz?
Her: I don't know ...