None of these answers work for me so I had to dig deeper myself.
If you are logged into CJ and go to Links -> Link Tools
they have a Deep Link Generator
. If you use that, you can see that all it does is append your current URL to https://www.anrdoezrs.net/links/<property ID or publisher ID>/type/dlg/
.
I tried URLs with query parameters and it does not appear that their tool does any sort of encoding. In fact, if I urlencode my original URL, it ends up in an infinite redirect.
Usage example: https://www.anrdoezrs.net/links/100298379/type/dlg/https://www.google.com/?q=cj