It depends on the citation format style you are using, and there are many styles to choose from. As reported in The Atlantic, the Modern Language Association (MLA) has stated that the correct way to cite a tweet in MLA format is as follows:
Last Name, First Name (User Name). "The tweet in its entirety." Date, Time. Tweet.
For example:
Athar, Sohaib (ReallyVirtual). "Helicopter hovering above Abbottabasd at 1AM (is a rare event)." 1 May 2011, 3:58 p.m. Tweet.
For additional details, view the online article in The Atlantic here. Please note that if you are using EndNote software to generate your references, many journal output styles may not yet accommodate citing a tweet. If you need assistance, please contact the Research Medical Library at 713-292-2282 (internal ext. 22282).
Article cited:
Madrigal AC. How Do You Cite a Tweet in an Academic Paper? 2012; http://www.theatlantic.com/technology/archive/2012/03/how-do-you-cite-a-tweet-in-an-academic-paper/253932/. Accessed December 2, 2013.
