Creating a Twitter feed on your website is easy whether it’s on WordPress or a normal website.
Twitter provide an easy to use way to do this and in this WordPress example WordPress provide a very easy way to install it.
There are WordPress plugins for this but really they are not necessary. In my opinion it is better only to install the plugins you really want and/or need on WordPress. Don’t get me wrong, I like plugins but too many plugins or some not very good ones can cause problems.