While you should make sure to post regular status updates as well, posting links can draw immediate traffic. What will happen is your link will be sent out to all of Twitter for anyone to see. If you have relevant keywords in your links, other users will click on your link and go to your site.
Assuming that the link is a useful one, it could be re-tweeted, or sent as a Tweet by a particular user to their followers. This could really be big if an influential follower gives you a re-tweet. If Bill Gates were to notice you and give you a mention, it could be a boon for traffic.
Engage Other Users In Conversations
You don’t have to be a chatterbox on Twitter, but you should be engaging your audience and talking to them. A simple re-Tweet of a product promotion, or acknowledgement of a follower’s promotion at work would be good enough.
Whatever makes your followers feel like you care and that you are important. Besides, if you never talk to your followers, why would they be interested in you? The more you talk to people, the more they get to know you and can recommend others to follow you. All the while, you become a go to source for information, or your site becomes a recommended place to visit.
The SEO value of Twitter cannot be denied. The more links you are able to generate, the more traffic your site is going to naturally get. This is because backlinks, or links back to your site, are seen as a good thing by Google and other search engines.
These links make search engines think you are an authority, or that others like your site, so they will rank it higher in search results. Most searchers on the Internet will only click on sites on the first page of results, so being among the top results will get you more traffic.
Keep in mind as well that there is SEO value in your bio and other information that you put into your Twitter account. If you have good keywords and relevant content, your Twitter page can potentially be ranked quite high as well.