Does Let's Encrypt have its own web-form to get a certificate?

Just to clarify, it's a website using the ACME protocol, not a partner website.

No they don't, and for the explanation: Web browser based ACME clients - #4 by jsha ; client-options: document inclusion/update policy. by cpu · Pull Request #377 · letsencrypt/website · GitHub ; ACME Client Implementations - Let's Encrypt