The quantum oscillatory magnetization M of a two-dimensional electron system in a magnetic field B is found to provide quantitative information on both the Rashba- and Dresselhaus spin-orbit interaction (SOI). This is shown by first numerically solving the model Hamiltonian including the linear Rashba- and Dresselhaus SOI and the Zeeman term in an in particular doubly tilted magnetic field and second evaluating the intrinsically anisotropic magnetization for different directions of the in-plane magnetic field component. The amplitude of specific magnetic quantum oscillations in M(B) is found to be a direct measure of the SOI strength at fields B where SOI-induced Landau level anticrossings occur. The anisotropic M allows one to quantify the magnitude of both contributions as well as their relative sign. We use realistic sample parameters and show that recently reported experimental techniques provide a sensitivity which allows for the detection of the predicted phenomena.
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