We investigate magnetoexcitonic states in the Ga_{1−x 1}Al_{x 1}As/GaAs/Ga_{1−x 2}Al_{x 2} As quantum ring with the Winternitz-Smorodinsky confinement potential. A homogeneous magnetic field is directed perpendicularly to the ring plane. The Coulomb interaction between the electron and hole is assumed as weak and is considered in the framework of perturbation theory. Obtained results show that the more realistic Winternitz-Smorodinsky confinement potential, which takes into account a peculiar smoothing of the confinement potential profile, leads to raising of the electron energy levels as compared to the case of a finite-height rectangular confinement potential.