Use the person's twitter "handle" as the author. Since tweets are short, include the tweet in its entirety. Include the date and time posted, as well.
@realDonaldTrump. "Wow, the Fake News media did everything in its power to make Republican Healthcare victory look as bad as possible. Far better than Ocare!" Twitter, 5 May 2017, 4:22 p.m., twitter.com/realDonaldTrump/status/860635815277453313
*Remember to omit the http:// and https://