Unified Police Authority says the man is stranded, but not injured and is in no immediate danger. He is dehydrated near the peak, waiting for search and rescue crews to guide him down.
A helicopter was working the scene, but was grounded due to low light.
Officials say it could take up to six hours to complete the rescue.
Corner canyon is accessed from the Orson Smith Trailhead near 13800 South 2060 East in Draper.
Copyright 2015 Nexstar Broadcasting, Inc. All rights reserved. This material may not be published, broadcast, rewritten, or redistributed.