I guess there is now.
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). For example:
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.
Setting aside the whole issue of why you would want to cite a tweet, this is not a well thought-out format. It assumes way too much: it ignores other potential microblogging media, like Mastodon, and assumes that there is only one such service, Twitter, and that the username is sufficient to identify the source. As the article I lined to mentions, there ought to at least be a URL associated with the citation — otherwise, you have to go to the service and search to find that specific set of words. And Twitter search is terrible.
Oh, well, there’s an easy way around this limitation: don’t dignify Twitter with formal citations.