There are strong experimental evidences of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state formation in layered organic superconductors in parallel magnetic field. We study theoretically the interplay between the orbital effect and the FFLO modulation in this case and demonstrate that the in-plane critical field anisotropy drastically changes at the transition to the FFLO state. The very peculiar angular dependence of the superconducting onset temperature which is predicted may serve for unambiguous identification of the FFLO modulation. The obtained results permit us to suggest the modulated phase stabilization as the origin of the magnetic-field angle dependence of the onset of superconductivity experimentally observed in (TMTSF)$_{2}$ClO$_{4}$ organic conductors.
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