I have found two companies so far that pay you for tweeting and am currently on the search for more.
I joined Sverve about a year ago and love them! They pay you a cent per every hundred followers you have so it definitely pays to increase your followers. I began making 13 cents per tweet and am now making 37 cents.
You have to check daily for new opportunities and if they have a Twitter campaign available you can participate once every 24 hours - and you just simply need to click the tweet button and your automatically credited the money.
Sverve also offers YouTube, Pinterest and blog opportunities as well as a referral bonus so please use my link and join Sverve here :) And there payout is only $5 - paid by PayPal.
Izea works a little differently - you have to bid on Twitter opportunities and they generally pay about $1 per tweet however some pay a lot more I once received $5 for one tweet!
A free Izea account allows you to bid on 5 opportunities (Twitter, YouTube or blog posts) per month. Or you can upgrade to unlimited bids for $1 a month. However I still have a free account - some of the blog post opportunities do not pay very much.
And you can check out my post on How to increase Twitter Followers to receive more per tweet or to be considered for more opportunities.
Please leave a comment if you know of any other Twitter opportunities - as I am always looking.Thanks!