In a sense, that is what a circumstellar disk is.
Source: European Southern Observatory (ESO)
These are usually most noticeable around young stars as protoplanetary disks, disks that form planets. In the picture above, the gaps in the "rings" likely represent forming planets, similar to how the gaps in Saturn's rings indicate the presence of moons.
Our own star has a few "rings", though likely not as visually impressive: the asteroid belt, the Kupier belt, the scattered disk, and the Hills cloud.
That said, there are differences between these structures and the ring systems we are familiar with from planets. For example, rings are made of solid particles whereas protoplanetary disks contain a lot of gases. Rings may exist around "mature" planets, whereas protoplanetary disks represent an immature phase of planetary systems. Protoplanetary disks are not visible to the naked eye, whereas ring systems may be. In technical terms, a circumstellar disk is not a ring system.