The whois
RFC describes the protocol as a TCP connection over port 43
(and not HTTP).
The protocol was originally designed to be a simple way to get information about a domain and there is no notion of encryption. This is not surprising, given it doesn't even consider the privacy implications of transmitting emails as part of the response.
Long story short, there is no way to transmit the information over an encrypted connection. Some registries may provide alternative implementations of the whois protocol over different protocols (such as HTTP), but it's completely up to the registry.