The rings of Saturn and Jupiter are circular. Orbits can be elliptical, so can rings be elliptical?
Short answer: no.
There are many collisions within ring systems, and collisions always work, over time, to push orbits to a circular shape (or destroy the rings). Any deviations tend to be quickly corrected.
For the same reason, rings tend to be extremely flat and extremely thin. E.g. Saturn's rings are only dozens of meters thick; given their diameter of 300 thousand kilometers, if you cut a model of the rings from ordinary size printer paper, the paper model would be too thick. (would not represent the thickness of the rings to the correct scale)
Another characteristic of rings is that they are equatorial. If they are not in plane with the equator, precession will drive them towards that configuration.
You could apply a perturbation that makes a ring non-circular, or non-flat, or non-equatorial, but then the system will quickly evolve towards circular, flat, and equatorial (or will be destroyed).
Rings are made up of a large number of individual particles, each in elliptical orbits. We see rings as circular because we don't see and follow the individual particles just the overall swarm of particles. Their individual orbits average out and just appear are a circle.
The individual orbits are constantly being changed due to collisions between particles, and gravitational influences for moons. Saturn's F ring is a good example of this. As can be seen from the images the ring is not a circle.