You bet you can. Twitter is a great tool for building a following and developing your very own community. In addition, you can use your profile and tweets to build backlinks to your web pages.
So how does it work? First, lets start with your Twitter profile. Your profile is important for a number of reasons including the fact that others may seek you out based on the contents of your profile. Make sure to include appropriate keywords that you want others to associate with you.
The second and most important aspect of Twitter is sending tweets. When you post a tweet, it is recorded on Twitter.com. If it includes a link back to your site, that works in your favor. Additionally, as other retweet what you have posted, it's noted on their Twitter accounts as well. The more backlinks you generate to your website the better.
One idea is to think about creating valuable content or a download and make it available on your web site. Tweet about it with a direct link others can use to access the information. As your followers retweet the information, you'll be building valuable link juice and improving your rankings.