To earn money from twitter you have to be a consistent and popular twitter user. Twitter as immense potential .
Earning money by posting tweets to your timeline is infact possible. But for earning money you need have good number of followers. The more the number of followers the more per tweet you can earn. You can define which add to post, how many ads per day etc
But post such tweets will lower your influence on twitter and you may loose followers so I suggest you have an additional account for earning money. Earning money from twitter can be like direct earning via advertising and affiliate marketing .
Hare are a few Sites where you can register to earn

ad.ly

Magpie - Twitter Advertising - Home Page

sponsoredtweets.com

Adf.ly

Twittad Let Your Ad Meet Tweets