Yes, Jupiter does have a ring system around it, but it is much fainter and smaller than the rings of Saturn. Jupiter's rings were first discovered in 1979 by the Voyager 1 spacecraft.
The main ring is broad but very thin, extending about 20,000 miles from Jupiter but only measuring around 30 feet thick. Jupiter also has three other narrow rings. The material in Jupiter's rings is thought to have originated from small moons that orbit nearby.