I'm never a fan of embracing technology for technology's sake, but I do love a good technological solution to a teaching problem, and I have found some technology is an absolute boon to engaging introverts.
It helps, of course, to understand what the heck an introvert is. Introverts aren't necessarily shy, and don't hate all human contact. But interaction is work. The classic distinguisher for extroverts and introverts-- two people go to a party, where both mingle and talk and have a good time with all the folks in the room, but the extrovert comes out pumped up and ready to go do something else, and the introvert emerges wrung out and ready to settle into his own chair in his own room in his own home by his own self.
Some extroverts really don't get introversion and suffer from the notion that introversion is a problem that needs to be solved. This can be problematic in a classroom; many introverts can tell you a story of some extroverted teacher who decided to force the introvert to come out of her shell, or to get more engaged with the other students in the room.
When I take a test like, say, the Myers-Briggs inventory, I peg the introvert-o-meter. But I've been a performing amateur musician my whole life, and I was a union president. Your introvert students can do everything that your extroverts can; they just may approach it a bit differently.
Years ago I discovered Moodle, an open-source learning platform. One of its features was a discussion board that allowed threaded conversations. It was handy for any number of classroom activities, but its most powerful feature in my class was discussion. Moodle has a discussion board feature that allows for threaded conversations, and for some of my students, this was a dream-- they could say everything they wanted to say without having to navigate the challenges of group social interaction. Students who had previously had little to say in class now had a great deal to say. Moodle also allowed me to turn on a feature that let the students "score" each others' responses. This was helpful for cutting back on. "Yeah, what he said" posts, but it also underlined the fact that some of my students who weren't adept enough to earn social capital by live meatworld interactions were now earning it by the quality of their writing and reasoning.
For introverts, social interaction is work. As teachers, we often imagine that the social interaction piece of an assignment is not really a real factor, like having point on your pencil or knowing how to sit in a chair. But for introverts, removing the work of social interaction can help them focus on the work of developing an idea or solving a problem.
I'm not suggesting that we shuffle all of our students off to isolated cages or walled-in computer stations. That would be stupid. But just as some teachers try to accommodate different learning styles, it's helpful to remember there are different social styles, and that, for example, deciding to do an assignment as group work is not a break for all of our students-- for some it's more work, not less, to navigate that situation.
Introverts don't need to be fixed and we don't need to be coddled. We don't need to be in an introvert-centered classroom. But it helps is we have a teacher who recognizes how we interact with the world and other humans. It's just one more way that students can be different and teachers can help by recognizing that the differences exist as something other than a problem.