If you’ve recently upgraded Wordtwit, you’ll notice some changes which are specifically to address the old Twitter API being deprecated. You will need to create a Twitter Application for Wordtwit to be able to add a Twitter account.

The developer has provided some instructions on how to correctly create a Twitter application for Wordtwit:Creating a custom application for WordTwit

Make sure that you set the callback URL to your websites URL, which is what I had skipped and caused the “Add Account” button under Twitter accounts to not function at all.