This is called pinning, and sometimes 'pinging'. A warning before a bite will almost certainly include this behavior, but it is also included in many other expressions that are not at all angry or violent so it depends very much on context.
I call pinning the avian exclamation point - whatever he's saying he's saying it with feeling and he means it.
Often parrots will pin when really excited, curious, when looking at a favorite toy or person, or when getting scratched in that perfect spot.
So pinning does not by any means mean that he is angry, but it does mean if he is expressing anger or agitation with the rest of his body that he is VERY angry.