Abstract: For extending the application fields of the acoustic radiation force and breaching the limitations on the type of the incident sound field and the geometrical shape of the scatterer in the existing theories,a generalized theory which is suitable for the calculation of the acoustic radiation force on an irregularly shaped Rayleigh scatterer in an arbitrary sound field is established.By concerning the curvilinear trajectory of the fluid particle's movement and the stochastic orientation of the scatterer's attitude,the typical theory for Rayleigh scattering is extended to account the translation and rotation movement of the scatterer induced by the first order stress of the sound field.Based on the velocity potential for the scattered field,calculating formula of the radiation force on an irregular scatterer in an arbitrary sound field is derived.Case studies show that for a regularly shaped scatterer in a simple type sound field the results using the method in this work are consistent with that in the literature,for irregular scatterers the angular speed is nonzero and the radiation force changes with the variance of the spatial attitude.