In order to configure Twitter, you must first create a Twitter app in order to obtain a Client ID and secret. You may do so at https://developer.twitter.com.
Create an App
From the Portal Dashboard, on the left navigation menu, click on "Overview" under the "Projects & Apps" menu.
Click on "Create an app" at the bottom of the page.
Enter your app name and then click "Next".
The next screen will show you your API key and secret key. Make note of these as you will need to input them into the TML Social settings on your site. When ready, click "App settings" to continue configuring your app.
Once on the app settings page, Click the "Edit" button next to "Authentication settings" at the bottom of the page.
On the authentication settings page, flip the switch to enable 3-legged OAuth. Flip the switch to request email address from users (this is required by WordPress).
For the next field, "Callback URLs", you will enter http://yoursite.com/login, or if using SSL, https://yoursite.com/login - where yoursite.com is the actual URL to your site. Also, if you are using a different login slug, the portion after the slash should match the slug you set up.
Fill out the rest of the required fields and then click "Save".
Configure Theme My Login Social
Now that you've set up your app with Twitter and obtained your API keys, visit your WordPress Dashboard, and on the main menu, click on "Social" under the "Theme My Login" menu. On this page, enter your API keys that you copied earlier.
Don't forget to check "Enable" and then click "Save Changes".
Login With Twitter
You will now see "Log in with Twitter" on your login form.