You will want to create an Input using the 'Poll an external website for JSON' connector. The workflow is very similar to polling an RSS feed for events. The difference is that the connector is polling a website for data, rather than an RSS feed, and is using a JSON adapter rather than an RSS adapter.
You might find the workflow documented on the thread esri-receive-features-rest-in helpful. But keep in mind that you will want to adapt the workflow to configure an Input to poll an external website for generic JSON, rather than receiving JSON posted to GeoEvent Processor.