While Twitter doesn't lend itself to deep conversations, there are still ways you can create a good impression and get results with it.
MediaBistro.com has a article on seven ways to network more effectively on Twitter. The full article is here.
Of course, it all starts with following the right people. Two other helpful suggestions are to retweet useful information, which I've mentioned here before, and to ask questions. It is an effective tool for peer opinions and to let people know what you're thinking about or working on.
I'm at twitter.com#cclarity if you want to follow me.