As far as I'm aware there is no bespoke JSON-RPC implementation but you can probably just define your own JSON-RPC service.
The easiest way to publish a service is through the "Published REST service" item in the desktop modeler, this way you can easily integrate your calls with the Mendix security.
Might also be worth looking into Mendix's Create a Rest API learning path
Hope this helps
Not long ago, a product manager of Mendix responded to a similar question in this thread. Looking at his reaction, you can simply publish a REST service with the parameters you require.