A couple of years ago a little piece of debris met my left eye. Later that day at night I started to notice a halo around streetlights as seen by my left eye. After an eye doctor visit and some treatment and time, they were gone for good. That made me ask myself the same question.
The rings are not around the street lights but in our views of them. Nearby rays coming out from the lamp are focused by your eye lenses to form a point in your retina. The halo you see is formed by rays that otherwise weren't aimed at your retina, but stuff refracted them midways and redirected them to your retina.
This could be by the droplets of water in the moisture of your glass (that's why cleaning it removed the halo) or by any other thing in the path of the rays. It is axially symmetric because only the rays that make a specific angle with the central ray get refracted into your eyeball, the rays at other angles get refracted elsewhere. And the refraction index marks this angle, which together with distance will give the perceived radius of the rings or halo.
As an experiment next time you can try to occlude with a finger the lamp and see if the halos are still there. Do you expect them to still be there for a) you inside your car, foggy glass? b) you outside your car?