One of the ways you can interact with your audience is by having contests with your audience. As I'm not a lawyer, you might want to consult one before stepping out of bounds with you competition (at least the rules from twitter on running a contest) Here are a few tools to help you:
Interactwive helps you to run your Twitter competition, removing the margin for error and handing control back to you. Let people enter your Twitter competition by mentioning your Twitter account. Optionally, limit further by requiring a link, phrase or hashtag to be included. Useful statistics are updated live. See tweets arrive the very second that they are tweeted. It is interested that this system can encourage people retweeting the same message which twitter does NOT recommend.
Twitrand is a great tool if you want to select a random twitter follower (or someone you are following).
Using this system, you sign in with twitter and you get a quick form
You select how many people to generate and enter an optional description.
twitrand will then generate a unique URL showing the exact time of the selection, your description and the results.
Tweet and share the link to prove your selection
Punchtab is not a twitter tool, but since we are talking about contests it needs to be mentioned. Punchtab can be used for many different types of programs. You can use it to create a customer loyalty plan where people earn points when they visit your site. This can then be used for giveaways. You can award badges for frequent visitors, as well as for people who consume your content. Pricing stars at free, and can become rather expensive ($99+). The free program lets you set up a loyalty program.
One Thing to Remember
Whatever you do, ensure that people must have to @mention your Twitter account in order to enter. You can still ask people to include #hashtags in their tweets, but including a @mention is absolutely essential.