Solid particles in Earth’s atmosphere, such as polystyrene beads, are an important factor affecting the processes of absorption and scattering of light in the atmosphere. These processes affect on the solar energy transfer in the Earth’s atmosphere, consequently they have influence on the regional and global climate changes and atmospheric visibility. In particular, great interest to study the scattering properties of small particles compared with wavelength, because of such particles experience low gravitational settlement and may have long time of life in the atmosphere. When scattering particle is much smaller than the wavelength of the scattered or absorbed light, this is the case of Rayleigh scattering. Scattering properties of these particles (such as intensity and the degree of linear polarization) at the Rayleigh scattering are simply derived from electromagnetic Maxwell’s equations. But when the particles are large enough to be comparable with the wavelength, the deviations from Rayleigh scattering law are observed. One of the clear manifestations of such deviations is the recently discovered quasi-Rayleigh polarization leap of monodisperse spherical particles. This quasi-Rayleigh polarization leap allows remote sensing of the sizes of distant particles, based on the spectral position of quasi-Rayleigh polarization leap at different phase angles of observation. In this paper, we studied the effect of the non-sphericity of a scattering polystyrene particle on the magnitude and position of the quasi-Rayleigh polarization leap. It is established that the non-sphericity shifts the position of the quasi-Rayleigh polarization leap shorter wavelengths. It is shown that for non-sphericity of particles makes the quasi-Rayleigh polarization leap becomes less pronounced. Moreover, it was found, that increasing of the phase angle and degree of non-sphericity shift the quasi-Rayleigh polarization leap position to shorter wavelength. However, in the case of not very elongated particles, the quasi-Rayleigh polarization leap is quite well manifested. Therefore, this method is suitable for remote sensing not only the size, but also the degree of non-sphericity of the scattering particles. A simple formula has been obtained for polystyrene beads that relates the degree of non-sphericity of a particle with the wavelength and phase angles at which the quasi-Rayleigh polarization leap is observed.