There are no UI elements in the Twitter framework except the Tweet Sheet (TWTweetComposeViewController). The Twitter login UI is in the device’s Settings application.
The recommended approach:
You can check if the user is already logged in via a call to +[TWTweetComposeViewController canSendTweet]. If this call returns false, the system will instruct the user to go to Settings.app and enter credentials when you call -[ACAccountStore requestAccessToAccountsWithType:]. In Settings, the user can signup or enter his or her credentials but unfortunately, the user is not redirected back to your app after logging in. As such, you may want to message the user to let them know to return once they have added an account.
It is still possible to create your own login sheet and then create the ACAccount instance for the user, but you will need to design and implement the login screen.