We investigate the photodetection properties of individual core/shell GaAs/AlGaAs nanowires (NWs) and, in particular, their behavior under linearly polarized light. The NWs are grown by Au-assisted metalorganic vapor phase epitaxy and electrical contacts are defined on NWs by electron beam induced deposition. The spectral photocurrent of the single NW is measured and the dependence of the polarization anisotropy ρ (varying from ∼0.1 to ∼0.55) on the absorption wavelength is found to be clearly affected by the core/shell structure. High quantum efficiency values (10% at 600 nm) are obtained which are attractive for a wide range of optoelectronic devices.