Squid can accept regular proxy traffic using https_port in the same way Squid does it using an http_port directive. Unfortunately, popular modern browsers do not permit configuration of TLS/SSL encrypted proxy connections. There are open bug reports against most of those browsers now, waiting for support to appear. If you have any interest, please assist browser teams with getting that to happen.
Meanwhile, tricks using stunnel or SSH tunnels are required to encrypt the browser-to-proxy connection before it leaves the client machine. These are somewhat heavy on the network and can be slow as a result.