The influence of an external orienting field on reentrant phase transitions taking place in smectic A liquid crystals with positive molecular anisotropy of magnetic susceptibility is studied on the basis of a thermodynamic potential of the X-1,X-0 type catastrophe. Topological classification of bifurcation sets and phase diagrams of the model are performed. It is predicted the possibility of induction of reentrant phases under the action of the external field. Conditions for experimental observation of this effect are discussed.