In order to post social media graphics to Twitter, you will want to connect to Twitter through your Integration Settings menu.  

Click "Add Account" next to the Twitter Integration

You will be redirected to Twitter's website.  If you are not already logged in, you will be prompted to login.

Click "Authorize app" in the confirmation page to complete the connection to Twitter.

Once connected, you can disconnect by clicking the "disconnect" button next to the Twitter option in your integration settings page.