The IRC network will need to support SSL connections, and you would connect on a different port to the standard 6667. Maybe 6668, 6670 etc. It's a pretty simple setup to get mIRC running through SSL. Download, install and configure OpenSSL (the FAQ is quite good), then select the options in mIRC to use your newly created SSL cert, and change the connect port in server options.
Although unless all clients on the network are connected via SSL, your messages will still be sent to them in plain text form, thus negating the purpose of using SSL.