We demonstrate that the angular distribution of photoelectrons from a strongly polarizable target exposed to a laser field can deviate noticeably from the prediction of conventional theory. Even within the dipole-photon approximation the profile of distribution is modified due to the action of the field of alternating dipole moment induced at the residue by the laser field. This effect, being quite sensitive to the dynamic polarizability of the residue and to its geometry, depends also on the intensity and frequency of the laser field. Numerical results, presented for sodium cluster anions, demonstrate that dramatic changes to the profile occur for the photon energies in vicinities of the plasmon resonances, where the effect is enhanced due to the increase in the residue polarizability. Strong modifications of the characteristics of a single-photon ionization process can be achieved by applying laser fields of comparatively low intensities $I_0 sim10^{10}-10^{11}$ W/cm$^2$.
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