I've been thinking about your question for a week or so and have something for you. I am very typically aspie. I have tics, I stim. I can't read people well (see the body language thread in this subforum), but I have real friends, and have managed to move past the acquaintances phase in a few cases. Most people see how odd and broken I am and beg out at some point, but, for whatever reason, some have an interest in sticking around.
I think what moves the interaction into a possible real friendship is to do something for the person, just to help. In talking, you invariably learn things about people, and even if it's initially only centered around a common interest or circumstance, there is always something you could do for them or help them with, that comes to light. Conversely, sometimes accepting someones offer of help is how things move forward.
They can and often do turn you down, and that's OK. One can gain NOTHING in any endeavor without taking risk. They may accept in order to take advantage or use you, which you will discover quickly and then you can cut them off. Some, however, will accept help and then reciprocate strictly (still distancing you, but fair). Someone may, at some point, invite you further into their lives. You may be invited to their home, taken in to their confidence, or they might do something for you out of turn, showing trust, and a willingness to invest in you on their part. What I'm getting at is that opportunitities to build trust is the step you are looking for. Trust mutually earned and tested gains you a friend. This proces can be uncomfortable and scary. There will be trainwrecks (we are aspies, after all) and embarrassment, but are you willing to endure some of that to gain a friend? That's for you to answer by your actions. Good luck.