Twitter introduced new real-time tools for websites that enable you to embed any public timeline on your website. You can choose User timeline, Favourites, List , Twitter Search, hash tag as a source to your embedded timeline. These embedded timelines allow your website visitors to reply, re-tweet and favourite Tweets, follow accounts, tweet directly on the web page like commenting on a blog.
See how it look like on your website and tweet me below.
Go your twitter settings and choose Widgets to create a timeline for your website.