Yes. It's a numbered road. The road connects the park with Moab via Potash.
My first time to the White Rim, we took the road outlined below as we had some time to spare. When I reached the junction of the White Rim Road and looked up to the canyon wall I thought 'Shit! The map is wrong. It's a dead end.' But no, you go up a nearly vertical wall and emerge near the visitor center.
www.google.com
You can drive around Canyonlands on the White Rim. Most people that do the WR on bikes have sag vehicles that lead/follow them around. These pictures are a conglomeration from a few trips.
Looking down onto the Shafer road. There is no room for mistakes or nature forbid, a flat at speed.
Unexpected flora.
One of our camp sites.
Charcoal fire for the paella.
Every trip we had paella as one of the organizers was a chef as well as a rider.
My Taco on a climb. This was steep, but not tricky. Note the road in the distance from whence we came. Most of the challenges of driving were keeping your eyes on the road. Many places the road was the edge of a sheer drop. Others you had to deal with hairpins or sand. Another challenge was keeping ATF in the transmission.
One of the sag wagons managed to totally empty the transmission of fluid. The owner said 'You don't need 4WL, just 4WH will be enough.' Unfortunately that meant the tranny was working overtime to make the steep hills and it overheated forcing the fluid out the filler, apparently and stranding us for a day at site halfway around the loop trail.
I ventured out with my Taco to Moab with a riding partner to fetch a case of ATF. We left near first light and arrived back in the dark. I needed to use all my spare fuel to make it out. I seriously overestimated the mileage I'd get.
After refilling the AT with ATF, the truck made it out of the park. The owner designed the diaper (above) to catch any ATF that
might find its way out as the park service was upset that we'd 'dumped' a transmission full of fluid already. As it turned out, the tranny didn't lose another drop; the diaper was clean when we got back. Unfortunately, the truck needed to be towed somewhere between Moab and CO as the transmission finally gave up the ghost.
This is the road out at the west side of Canyonlands. It isn't nearly as imposing as Shafer, but it did get washed out at one point and closed the WR for a while.
This is one of the concrete repairs that they put in where erosion was obviously going to continue.
In SW style, junked cars dispatched off the side of the road.
Edit:
@Daniel is right on all accounts. It is a beautiful journey around the White Rim no matter how you do it. Some ride it in one day (insane). One time we planned for a day off and brought floating toys to enjoy ourselves in a not usual way on the ride.