I'm currently going to develop a REST API. I found Restler seems to be a good choice. But I'm wondering if it supports HTTPS? If YES, is there any example ?
Yes, it supports it. This is setup on your webserver.
nginx: http://nginx.org/en/docs/http/configuring_https_servers.html
apache: http://httpd.apache.org/docs/current/ssl/ssl_howto.html