Twitter was a social networking website on the Internet in the 21st century. The Eleventh Doctor wasn't fond of Twitter. (TV: The Girl Who Waited, The Power of Three)
References
In 2008, after hacking his way onto a videoconference with Earth's scientific elite, the Eleventh Doctor urged them to disseminate his computer virus via every electronic means available, including Twitter, to contact the Atraxi. (TV: The Eleventh Hour)
In 2009, after the Torchwood Three team accidentally drove off the Severn Bridge, they heard a mysterious voice under the water. Back at the Hub, Ianto Jones stated that it was a hit on Twitter. (AUDIO: Submission)
In 2011, a news reporter stated that "Miracle Day" had been "trending", terminology often associated with Twitter. (TV: The New World)
In the same year, Patricia Menzies said that her phone could not access Twitter. (AUDIO: The Crimes of Thomas Brewster)
When the Doctor's TARDIS arrived on Apalapucia and Amy Pond asked for her mobile phone, the Eleventh Doctor assumed she wanted it to update her Twitter, rather than to take pictures of the sights. (TV: The Girl Who Waited)
After a wave of mysterious cubes arrived on Earth, this new phenomenon received a thousand separate Twitter accounts within the first three hours of their arrival. Upon learning this, the Eleventh Doctor exclaimed "Twitter!" in an irritated tone. (TV: The Power of Three)
In 2013 the Eleventh Doctor seems to acknowledge Clara Oswald's joke that Twitter is basically, in the Doctor's words, "human souls trapped like flies in the World Wide Web, stuck forever" (the Doctor himself was actually talking about the "Something" living in the Wi-Fi) (TV: The Bells of Saint John).