Quantum rings subjected to a Rashba spin-orbit coupling and an external magnetic field possess interesting magnetic properties. Specifically, the spectral linewidth of magnetic susceptibility is found to be independent of the ring geometry. For zero spin-orbit coupling it varies linearly with temperature and the slope is proportional to a scaling factor of material parameters. When the spin-orbit interaction is switched on, there is a turning temperature below which the spin-orbit coupling strength is directly measurable. The upper bound of the turning temperature is also investigated.