CAA is not the record for this. As @schoen already replied, it is only used by CA's to check if they are allowed to issue a certificate to a domain.

But with DANE TLSA Resource Records you can pin a public key to a website. Alas the implementation of TLSA-RR checking in browsers is dependent on extensions at this time. I wish it was native in browsers with a big red sign when violated. When done in combination with DNSSEC it's very hard to fake certificates. Or more precisely asymmetric cryptography key pairs used by servers. Certificates for TLS would not be needed anymore if TLSA-RR's were standard practice. A company might still use a certificate to attest it's identity beyond internet domain ownership.

Edit: This is for TLSA 3 1 1 and 3 1 2 records. That's what I have experience with. Just read on Wikipedia a lot more is possible with TLSA-RR's including certificate and CA pinning. https://en.wikipedia.org/wiki/DNS-based_Authentication_of_Na...