We investigate the electronic properties of a semiconductor quantum ring with an elliptical shape and non-uniform height, allowing for distributed quantum-dot-like bulges along its perimeter. The adiabatic approximation and the finite element method are combined to calculate the allowed electron states in the structure under the effective mass approximation, considering the contributions from Rashba and Dresselahaus spin–orbit interactions and the Zeeman effect in the presence of an applied magnetic field. We discuss the features of the calculated spectra for two different ring geometries: a symmetric one with four dot-like bulges, and an asymmetric one with three hilled protuberances. The information about those states allows us to evaluate the linear optical absorption response associated with interlevel transitions between the ground and lowest excited states. This phenomenon takes place at resonant energies of only a few milielectronvolts. It is observed that spin–orbit interactions tend to quench this response under zero-field conditions in the case of symmetric confinement.