Format: 

Author, A. A. [Screen name]. (Year, Month Day). Title of document [Format]. Retrieved from URL

Examples: 

Gibson, W. [GreatDismal]. (2015, July 20). Finally read a bit about Mr. Robot. How on earth did someone not manage to stop them using that title? [Tweet]. Retrieved from http://twitter.com/GreatDismal/status/623319630115766272

In-text: (Gibson, 2015)

Notes: 

Include the author's screen name in brackets after the author's name. If only the screen name is known, provide it without brackets.

Source:
APA (ER) - p. 33, no. 74