Both structure and bulk inversion asymmetry in modulation-doped (001)-grown GaAs quantum wells were investigated employing the magnetic field induced photogalvanic effect. We demonstrate that the structure inversion asymmetry (SIA) can be accurately tailored by the delta-doping layer position. Symmetrically doped structures exhibit a substantial SIA due to impurity segregation during the growth process. Tuning the SIA by the delta-doping position, we can grow samples with almost equal degrees of structure and bulk inversion asymmetry.