Here are two methods that you can try to resolve the issue:
1.Use Terminal to Reset the Camera: Open Terminal (you could find it in your launchpad) and type the following command: sudo killall VDCAssistant and then enter your password when required. This command will reset the camera software. If this command doesn't work, you can also try typing sudo killall AppleCameraAssistant. To ensure effectiveness, you can restart your Mac after entering these two commands.
2.Reset NVRAM/PRAM: Shut down your Mac, then turn it on and immediately press and hold these four keys together: Option, Command, P, and R. Hold them for about 20 seconds. Your Mac might appear to restart. Then check FaceTime to see if the camera has been activated.