Everyone who has ever seen Saturn through a telescope is astonished to see the system of rings that surround it. Those rings are rock and ice that span thousands of kilometers around the planet. They are the hallmark of Saturn, but ring systems exist around Jupiter, Uranus and Neptune as well, albeit in less dramatic forms.
Yet, you shouldn't need to be a giant planet to have a ring. As long as debris accumulates in the gravitational well of a planet, the rotation will cause it to form a ring a debris near its equator. How you build that ring can come in many forms, but one method would be for an asteroid to get a little too close and get caught by the planet ... and then crushed by the tidal forces it feels thanks to the planets's gravity.