We study the behaviour of geodesics on a Randers rotational surface of revolution. The main tool is the extension of Clairaut relation from Riemannian case to the Randers case. Moreover, we consider the embedding problem of this surface in a Minkowski space as a hypersurface. Finally, we study the rays and poles as well as the structure of the cut locus of a Randers rotational surface of revolution of von Mangoldt type.
