This icalendar to event facebook application looks like it would do the trick. Use amr-events (or any such plugin) to generate a valid ics feed. Add that to the application and there you should have it – integration from your wordpress events into facebook .
Note: reviews seem to be polarised (very good or very bad), and it does have a lot of users. Note: I have found facebook very SLOW to update either way and can imagine this may cause some of the dissatisfaction. That said I am not using this application myself, just thought it might be useful.
Reverse direction?
To go the other way, you need
- a valid public facebook feed [warning: sometimes these appear to be troublesome] – see https://icalevents.com/4162-finding-the-facebook-events-ics-feed-for-subscribing-or-syncing/,
- and a plugin like amr-events or amr-ical-events-list (free at wordpress)
- Activate the plugin
- Drop [events ics=facebookicurl] or [iCal ics=facebookicurl] into a page.
- Publish!