Yes, Edward Snowden has recently signed up to Twitter. The account has been officially verified and Twitter itself has confirmed the account to be authentic. On the bio section, Mr. Snowden wrote "I used to work for the government. Now I work for the public." His first tweet reads ""Can you hear me now?" 
In what some consider to be humorous, one of the first groups Snowden followed was the NSA. At the moment, he is believed to be living Moscow, Russia, staying as far away from US prosecutors as possible.