Yes, Mogo, like all Green Lanterns, has a Green Lantern ring.
In most incarnations, it's kept deep within the surface of the planet. This has occasionally even been a plot point, as it is especially difficult to access or get close to Mogo's ring. For example, in the Green Lantern animated series episode "Homecoming", Saint Walker is forced to take drastic action to super-charge Mogo, because his effect on most Green Lanterns is based on proximity, which isn't possible given the location of Mogo's ring.
It's worth noting that, while the ring is usually shown as being a normal-sized ring (an inch or so in diameter), Mogo is often fond of creating an enormous ring as a construct around itself. While beautiful (and utterly badass), this is not Mogo's actual ring.