The proper word would be "tweeting" (see tweeting)
No, but I tweeted the post to my followers... - Guy 2
I think I'm going to be twittering this link to everyone I know! - Guy 1
It's called tweeting... - Guy 2
Nero twittered as Rome burned.
John: No, I'm tweeting that one more person who has no idea of what twitter is just commented on it.