Wordpress API usually is used with Akismet modules to prevent spam. You will get wordpress API when you've registered with wordpress.com hosting. The wordpress API key will be sent into your gmail.
But what if my email that contain wordpress API has been deleted? Should I need to register with wordpress.com hosting again?
You don't need to do that if you still can login the wordpress hosting. After login go to your blog then your profile or you can go to
Change [yourname] with your blog name. On that page, under Profile you will see
Your WordPress.com API key is: ....... Don't share your API key, it's like a password.
That's your wordpres.com API
If you can't login and your email that contain wordpress API has been deleted so the solution is register again with wordpress.com hosting and write down your wordpress API on a paper.