Does my iPhone camera have to be working to connect to my Apple Watch?

Yes. It's how your phone and watch connect the first time. If your camera isn't functioning, you need to get your iPhone fixed.

You can manually pair your watch,this doesn't need the camera;

Start by tapping the "I" button on your Watch"bottom right corner", which will bring up your device's name. Then on your iPhone, tap the device name that matches the one displayed on your Apple Watch. You'll see a six-digit code will appear, which you'll enter on your iPhone.

Then follow the onscreen instructions to finish pairing your watch.