Track how many times a JSON file is requested from other websites
There is a core module for that Statistics. On the configuration of this module (admin/config/system/statistics) you can ask for 'Count content views' who should work on every page drupal display (so your json).

There are a lot of custom module to extends statistics.

A little warning : Angular may be cache your json, so if your user go two times on a page you can loose this data. Maybe smarter to do this on the angular side.