How can I add a captcha to this HTML form
I'd say you have two obvious choices : 


either you reimplement the form using the drupal webform module and then add some captcha module like recaptcha,
or you keep going the tought html-only route and just see how you can integrate a captcha library within your "html within the content editor" form...


I'd say the first strategy is wiser. Particularly since your form is fairly straighforward.