The way I got over this kind of anxiety was to lead a study group in college. The people in the study group were already friends so it wasn't as stressing, but during the study group sessions, I made it my responsibility to lead the group. At first it was... unnerving, but definitely not as bad as it was with people I didn't know as well.

So maybe you should start with some friends that you're more comfortable with (not professional acquaintances) but in a different context than just hanging out?