1. Go to apps.twitter.com and sign in with a twitter account.

  2. Click the Create New App button.

  3. Enter a name and description for your forum.

  4. Enter http://forum.example.com in the Website field.

  5. Enter http://forum.example.com/auth/twitter/callback in the Callback URL field.

  6. Agree to the legal stuff and click the Create button.

  7. In the Settings tab, check “Allow this application to be used to Sign in with Twitter” and click Update Settings.

  8. In the Permissions tab, choose “Read Only” and click Update Settings.

  9. Click on the “Keys And Access Tokens” tab. The API key and API secret go in the twitter_consumer_key and twitter_consumer_secret settings in the Login section (/admin/site_settings/category/login).

Settings

Source: https://meta.discourse.org/t/configuring-twitter-login-for-discourse/13395