There are housings for using cameras underwater, somewhat overkill for just
rainy day use.
There are also glove-like arrangements that are a blank filter with a
plastic bag attached. The filter is mounted on the camera and the bag covers
the camera. Ypu reach inside the bag to operate the camera.
I've taken my old Canon FX out on rainy days many times. I dry it off after
use, set it in front of the air conditioner or heat duct for a while and it
still works just fine.

I'm going to make rain protector for my camera myself.
I will use raincoat and take part of that. You lens goes where
your hand normally goes and so on.
I will probably not look so professional but at least it should
work with longer lenses too.