Is it possible to integrate a custom Drupal donate form with CiviCRM?
So this is definitely possible.  I'm assuming that you asking the question, you have some Drupal FAPI experience.

If you have CiviCRM installed already check out the API explorer, and check out the Contribution entity, transact action

Documentation of this API is spotty to non-existent, but its powerful, and works.

There is actually a sophisticated example of using this API call for Event Registrations in the CiviCRM Entity project, CiviCRM Entity Price Field submodule
https://www.drupal.org/project/civicrm_entity

The code there is a little complex, and your requirements may be simpler, but come into the civicrm entity channel on CiviCRM's Mattermost chat at https://chat.civicrm.org and ping @jackrabbithanna and I can help you get started.