Currently STM does not officially support this. However, in theory, you could add the certificate as the default for the web service and add your CA certificate to the CA Certificate Store on the STM Server.
I need to state this very clearly: This is NOT a supported configuration.
Please feel free to uptick on the Feature Request here: Can Storage manager use a keystore that is not the "Self Signed" cert.
Voted on the feature request, thanks for the reply.