I have a custom registration field that I require uses to fill out when they register.

If a user registers via Facebook they are not prompted to enter this field.

Is it possible to force users who register via Facebook to fill in the field?

I faced this same dilemma with my board as I had a custom field to inquire on how they found us. The best solution for this is to use Required Info by @onlyME. This allows you to force the member after registration to complete said fields before they have access to your site. This will exclude members who registered manually.

Hope this helps!