@ + #
There are dozens of Twitter accounts for websites that publish only 140-character stories. Some of the most notable are @OneFortyFiction, @seedpodpub, @sixwordstories, @twitterfiction, @7×20, and trapezemag.
All, unfortunately, are unpaid markets. But if you just wanting to see your words on the internet highway, consider the above.
If your tastes run towards non-fiction, rather than fictional tales, consider adding #cnftweet. Each day, @CreativeNonfiction selects one tweet with this hashtag to retweet, and these tweets are then eligible to be included in upcoming issues of the magazine, or in their newsletter.
@Nanoism is a paying Twitter fiction market, which publishes three times a week and pays between $1.50 and $1 for stories: not bad, given the brevity of the form. Serialized Twitter fiction is paid out at a higher rate.
In short: keep on writing, and keep your eyes peeled for opportunities to grow your fan base. Depending on where you choose to publish your stories, your work may be exposed to thousands of people. In addition, there are often contests being held on Twitter by various publishers where you can win cash and prizes with your well-written, 140-character stories.