No, it couldn't.  Rings are unstable over long periods.  There are countless collisions taking place between the particles that mean the ring will always be slightly lumpy, and regions of higher mass will attract other debris by gravitational attraction and electrostatic charges.  These clumps will grow and grow, and attract each other until there are only a few large clumps left.  These bodies would be moons of the planet and might even coalesce into one moon.

Particles, and the resulting moonlits, would not have perfectly circular orbits, at least in part due to the collisions.  This means if any torus did form, it would also be elliptical and would quickly be broken apart by tidal forces squeezing it into the orbital ellipse.  It would surely be too fragile to survive the bending process.  Further gravitational stresses on the torus would come from any shepherd moons, such as Saturn has.  Also, a torus-moon would have a high surface area for it's mass, and micrometeor impacts, sunlight, and cosmic radiation would break the surface down into powder.  The powder would only be weakly bound by gravity and would probably drift off to form another ring.

Still, there are many things we thought couldn't exist then we found them.  Hot jupiters for example.  So never say never in science.