There are a few ways, some easy, some not, are you admin on the website?
RTSP streaming will allow you to display an image on a website with a 'little' effort' needed, or you can use the likes of angelbox if you have a RPi spare.
You can also use a pc to stream using the likes of OBS to youtube and then embed the stream into a website, this gets around a few security issues.
Not trying to be a dick, but there are MANY ways to do this, and some depend on your skill and access to the items, so a little more info would be needed.
We've tried the OBS to Youtube method and it seemed to work pretty well. There was a 10-15 second delay. We didn't stream it to a website though. I would imagine that this would require a wordpress template that supports live streaming, but I could be wrong.