Why don’t you show how relevant you are to your site visitors and get more followers on twitter? Once they start following you, you can start pointing them to your website again and again now that you have their attention.
Unfortunately there isn’t a simple way to create this block from the existing drupal modules. The procedure to create a Twitter block is very convoluted using Views and what not.

But first, a little rant. It seems like a lot of developers are more focused on being ‘standards complaint’ (politically correct) than create easy to use software as if they create software for other developers.
“Oh! let’s not rehash the code here, that’s not good core re-use. Let’s ask users of our module to download and install 10 other modules on which we will base this module!”
This block is installed through the module (download below).
The block is highly customizable. Check out the options you have in the administrator’s interface.
This interface is found in Administer > Sites Building > Blocks > Twitter Block [configure]

The blocks can be theme using css as each element is enclosed in a <div> of appropriate name.
Download
Click here to download the module.
Installation Steps
1. Install the Module: Just place the module in the modules directory of your drupal site or sites/all/modules/ directory if you have multiple installations. Log in as administrator and go to Site Building > Modules. Scroll to the bottom and find “Other” package. Expand it, check the TwitterBlock one and click Save Changes.
2. Place The Block In A Region: Now go to Administer > Site Building > Blocks. At the bottom of the list you will find Twitter Block. Drag it to the required region and click Save Changes.
3. Enter Username/Password: Once you click save, you will still not see the block, you must enter the username and password. So click on ‘configure’ next to Twitter block and enter your username and password. Choose a appropriate update frequency and click Save.
You’re all done. Your module should be working now. Leave a comment on this post regarding bug fixes and other issues.
License
This module is provided under the GPL license. Read the full version here.