Hi,
The Facetime app Help menu (type in "Camera") confirms that an external camera can be used with Facetime. So as long as your camera is compatible with your Mac, and you use the proper cable connection, your camera should be recognized when you select the Video item in the Facetime menu. You might check the Apple website for iMovie compatible camcorders as being perhaps applicable to Facetime as well.
https://support.apple.com/en-us/HT204202
What steps are you taking to get Facetime to recognize your camera, and what happens when you try them?
-- Rich