How to create an app that will allow to register in twitter and return captcha image as validations



Please let me know is there any API which will support to register user in twitter my website?
when I will enter details like username, email id, and first name and last name then API will allow me to create account with these records and return captcha for final processing.
Please have look on this demo.
I want similar functionality as the give url.

Please provide me some help on this.