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Ti substituting Ru in Sr_{2}RuO_{4} in small concentrations induces incommensurate spin density wave order with a wave vector Q≃(2π/3,2π/3) corresponding to the nesting vector of two of three Fermi surface sheets. We consider a microscopic model for these two bands and analyze the correlation effects leading to magnetic order through nonmagnetic Ti doping. For this purpose we use a position-dependent mean-field approximation for the microscopic model and a phenomenological Ginzburg-Landau approach, which both deliver consistent results and allow us to examine the inhomogeneous magnetic order. Spin-orbit coupling additionally leads to spin currents around each impurity, which in combination with the magnetic polarization produce a charge current pattern. This is also discussed within a gauge-field theory in both charge and spin channel. This spin-orbit coupling effect causes an interesting modification of the magnetic structure if currents run through the system. Our findings allow a more detailed analysis of the experimental data for Sr_{2}Ru_{1−x}Ti_{x}O_{4}. In particular, we find that the available measurements are consistent with our theoretical predictions.