Official MLA Twitter Citation Format – Taken from MLA Site
How do I cite a tweet?
Begin the entry in the works-cited list with the author’s real name and, in parentheses, user name, if both are known and they differ. If only the user name is known, give it alone.
Next provide the entire text of the tweet in quotation marks, without changing the capitalization. Conclude the entry with the date and time of the message and the medium of publication (Tweet).
Athar, Sohaib (ReallyVirtual). “Helicopter hovering above Abbottabad at 1AM (is a rare event).” 1 May 2011, 3:58 p.m. Tweet.
The date and time of a message on Twitter reflect the reader’s time zone. Readers in different time zones see different times and, possibly, dates on the same tweet. The date and time that were in effect for the writer of the tweet when it was transmitted are normally not known. Thus, the date and time displayed on Twitter are only approximate guides to the timing of a tweet. However, they allow a researcher to precisely compare the timing of tweets as long as the tweets are all read in a single time zone.
In the main text of the paper, a tweet is cited in its entirety (7.4.1):
Sohaib Athar noted that the presence of a helicopter at that hour was “a rare event.”
or The presence of a helicopter at that hour was “a rare event” (Athar).
The APA Style
APA has not as yet come up with a solid rule, but they have a link to some examples of how social media can be cited.
How do you cite Twitter? – Taken from APA’s site
Because posts from online social media, such as Twitter and Facebook, are not yet often fodder for scholarly research, specific reference examples aren’t included in the Publication Manual. However, some examples can be found in the Social Media section of the APA Style Blog.