Is it possible to connect the iPhone camera to Safari or another web browser?

The iPhone camera can be used with any app that uses cameras on a Mac over continuity.

What are you trying to use it with in Safari exactly?

The software you are using within Safari would need to be able to switch between camera options available to the Mac which include the iPhone's camera.

It will come down to the service or website trying to find the camera wether it can see it or not.