Q. How do I cite references from Twitter and Facebook in an academic paper?

From the APA Style Blog:

To cite a Twitter or Facebook feed as a whole or to discuss it in general, it is sufficient to give the site URL in text, inside parentheses. There is no need for a reference list entry.           

President Obama uses Twitter (http://www.twitter.com/barackobama) and 
Facebook (http://www.facebook.com/barackobama) to keep citizens up 
to speed on his initiatives, especially health care reform and Supreme 
Court nominations. 

To cite specific posts from Twitter or Facebook, you would follow the format for citation of online sources (see pp. 214–215 of the APA Manual, 6th edition. 

Here are some examples of reference list citations (APA) from Twitter:

BarackObama. (2009a, July 15). Launched American Graduation Initiative 
 to help additional 5 mill. Americans graduate college by 2020: 
 http://bit.ly/gcTX7 [Twitter post]. Retrieved from 
 http://twitter.com/BarackObama/status/2651151366 

Astro_Mike. (2009, May 20).  From orbit: We see 16 sunrises and sunsets in 24 hrs, each one spectacular as the sun lights up the atmosphere in a spectrum of colors [Twitter Post]. Retrieved from 
https://twitter.com/Astro_Mike/statuses/1852218149

And here is a citation using MLA:

Massimo, Mike (Astro_Mike) "From orbit: We see 16 sunrises and sunsets in 24 hrs, each one spectacular as the sun lights up the atmosphere in a spectrum of colors" 20 May 2009, 3:36 a.m. Tweet.

Here is an example of a reference list citation from Facebook:

Barack Obama. (2009b, October 9). Humbled. 
 http://my.barackobama.com/page/community/post/obamaforamerica/gGM45m 
 [Facebook update]. Retrieved from http://www.facebook.com/posted.php? 
 id=6815841748&share_id=154954250775&comments=1#s154954250775 

Here is an example of the in-text citation for the Facebook reference:

President Obama announced the launch of the American Graduation Initiative 
(BarackObama, 2009a). He also stated that he was “humbled” to have 
received the Nobel Peace Prize (Barack Obama, 2009b).