Signalfade

Adds a new type of feed you can subscribe to. 
 http://example.com/feed/json or <code>http://example.com/?feed=json</code> to anywhere and you’ll get JSON back.

JSON Feeder

Adds a feed based on the jsonfeed.org standard that one can subscribe to or parse.

Jeroen Sormani

Pinecast

This plugin allows you to sync your Pinecast podcast (or any JSONFeed-compatible podcast) with your WordPress blog.
Please see Pinecast’s <a href="https://pinecast.support/en/articles/3072843-pinecast-wordpress-sync-plugin" rel="nofollow ugc">support website</a> for more information.
After installing, visit Settings > Pinecast to add feeds. Add your Pinecast RSS feed URL (found on your podcast dashboard), along with the podcast’s name (for your reference), categories that you wish to be applied to each episode’s post, and whether you’d like to include episode artwork in the posts. Save changes.
Once your podcast is added, you can press the Sync button to import episodes. Episodes will sync automatically every hour.

Pinecast WordPress Sync

This plugin allows you to sync your Pinecast podcast (or any JSONFeed-compatible podcast) with your WordPress blog.

JSON Feeder vs Pinecast WordPress Sync