Right from the New Model Single Six owners manual: Page 16
DRY-FIRING: Going through the actions of cocking, aiming, and pulling the trigger of an unloaded gun is known as “Dry Firing.” It can be useful to learn the “feel” of your revolver. Be certain the revolver is unloaded and that the gun is pointing in a safe direction even when practicing by dry-firing. The Ruger New Model revolvers can be dry-fired without damage to the firing pin or other components.
Right from the Ruger revolver FAQ:
Can I dry fire my Ruger revolver?
Yes. All Ruger revolvers can be dry fired without damage, and dry firing can be useful to familiarize the owner with the firearm. However, be sure any firearm is completely unloaded before dry firing!