My advice would be to stop thinking of yourself as an "introvert" and understand that you're probably somewhere in the middle, like most people. Figure out what kind of social context you like and gravitate to that. Don't assume because you're an "asian engineer" that the best fit for you is that stereotypical social context. I'm a first generation immigrant, went to math/science high school, went to engineering school, but half my friends are public interest lawyers. I gravitate to that personality type. Your words suggest that you put yourself in a box, but that doesn't have to be the case.
Also, don't assume you're "awkward." Maybe you are, but here's a secret: a lot of the people you think of as "socially normal" simply have a head start by virtue of having grown up in this culture. There's a lot of forced childhood socialization that immigrants miss out on: church, block parties, etc. My wife used to go to cornfield parties as a kid in Iowa. That kind of low-key, parentally-supervised, non-threatening socialization helps build basic skills, but its something immigrant kids often miss out on because their families don't feel comfortable participating in the community.