The act of creating a mob on Twitter by tagging a multiple people in a post. The purposes of a Twitter Orgy is typically to get those tagged to respond to your post.
It is akin to a person IRL muttering to themselves loudly in public with the hopes of people hearing them and engaging with them.
It is a cheap form of attempting to engage people.
@Mary was looking for people to gang up on @Steve, so she started a Twitter Orgy and tagged half of the school in her post about him.