The handle is held in place in the cam by a set-screw. You can access it through a window in the side of the extrusion that the arms slide in -- takes an Allen key, not sure what size.
I haven't tried it, but I expect you'd be able to loosen that set-screw, rotate the handle with respect to the cam, and lock it down again -- though you might have to grind a new flat for the set-screw to lock against.