Yes, citing Tweets is acceptable in academic papers (especially in certain research areas like: social media; new media; news & politics; technology; etc.) but why cite it differently from “traditional” web resources? That’s the way they’ll be retrieved 99.9% of the time. Citing them as a sparate type of media is a bit shortsighted and opens up the door for other proprietary categorizations of media type (iTunes App; Facebook Status; “Like”). Plus, the current citation doesn’t even include a URL, ID, or any other way to actually find the tweet - only the date, and at that, it’s the date given in the *reader’s* time zone.
Ugh, so many things wrong with that approach. This is what happens when people who don’t understand technology derive standards based upon those technologies. (I’m looking at you, Congress.)