The cast of Twilight does have a presence on Twitter. But, don't be fooled by the fakers out there. Robert Pattinson and Kristen Stewart do not have a twitter account.
Here are the verified accounts of some of the cast:
Peter posts often and really gives details of where they are in production or what he has been up to in relation to the production of Twilight (ie. he tweeted: "Just got back from dinner with Elizabeth, Nikki, Kellan, and Taylor.Who says Werewolves and Vamps can't get along. Tmrw more fight training.")