Rothman can be found in Broken Valley, in a dead-end canyon near the Southern Valley shrine.

He is easy to miss as he is not on the surface and so you cannot see him from a distance. Rothman is in a hole, or to be precise a Troll-hole, and can't get out. Approaching the hole will trigger a cut-scene and give you the side-quest Stuck in a Hole which, simply, is to rescue Rothman. To do this you will need some rope.

You can mindread him for 100 exp, from which you will hear Rothman praying to the Divine, and promising to attend church if he ever makes it out alive.

Once you free Rothman, a Troll will appear. Once it is dead Rothman rewards you with Rothman’s Bow, explaining that he is giving up the life of a hunter and going back to the safety of home.