The APA Publication Manual does not give specific guidance on how to do this. This is an evolving area, and these suggestions were created by the APA Style Blog. There you will see guidelines for all social media.
Here are some examples of individual tweets and how to cite them.
Tweet, Individual Author
Gates, B. [BillGates]. (2013, February 26). #Polio is 99% eradicated. Join me & @FCBarcelona as we work to finish the job and #EndPolio. VIDEO: http://b-gat.es/X75Lvy [Tweet]. Retrieved from https://twitter.com/BillGates/status/306195345845665792
In-text citation: (Gates, 2013).
Tweet, Group Author
Stanford Medicine [SUMedicine]. (2012, October 9). Animal study shows sleeping brain behaves as if it's remembering: http://stan.md/RrqyEt #sleep #neuroscience #research [Tweet]. Retrieved from https://twitter.com/SUMedicine/status/255644688630046720