Hey there, RAMiller501!
Thanks so much for using Apple Support Communities.
We can definitely understand wanting to record your FaceTime calls. However, as of right now there is no built-in way to do that. You can capture the video of your FaceTime call using the screen recording feature of your iPhone but that will not contain the audio. If you had any sort of audio recording equipment or even another device that records audio (iPhone, iPad, etc) then you could record the audio separately. Those files could then be synced in an app such as iMovie.
We're going to share some resources below that should help:
Record the screen on your iPhone, iPad, or iPod touch - Apple Support
Make a recording in Voice Memos on iPhone - Apple Support
iMovie User Guide for iPhone - Apple Support
We hope this is helpful.
Cheers.