If you would like to have posts to your Twitter account come in as tickets then you can enable that feature known as your Twitter portal
How does it work
If you would like to turn Twitter Mentions into tickets you can turn on your Twitter portal and any new mentions will come in as tickets just like they would through your web or email portal.
A basic setup of this would be creating a Twitter account dedicated for just support for your company. Once you do that all you have to do is get your developer account with Twitter and set it up with SeamlessDesk. You can read on to learn how to setup your portal.
How to setup your Twitter Portal
Unlike Facebook where you can only use a Facebook page for your support portal, Twitter you can use a regular account. It is best practices to dedicate a Twitter account for support.