The built-in authorization types should cover most of your authorization needs, but you can also use the legacy HTTP Authorization method. This kind of authorization is done by using authentication forms on a web page. To use API calls, you typically need to launch a browser, log in to a web form, and then establish a session.
In ReadyAPI, you can create an HTTP Request test step to provide your credentials (username, password, method). To make the authorization persistent, enable the Maintain HTTP Session setting.
You can find an example of creating HTTP authorization in the HTTP Authorization Tutorial.