Startup Adjix has a way to monetize on your Twitter account by adding short text ads to the end of your tweets. It works by selecting from options of different ads, and then when you send out your tweet, the ad link shows up at the end of your message, clearly marked as an ad.
Payment is based on your number of Twitter followers and the bid price from the advertiser. For example, if a Twitter user has 1,000 followers and the advertiser is willing to pay $0.50 CPM, the user would earn $.50 for that tweet.
There is more information on the specifics here, and you can also watch a video demonstration.