Raman scattering of light (RS) on an array of oriented silicon nanocrystals was studied experimentally. The angular dependence of the intensity of the polarized components of the RS was measured and the parameter of the degree of polarization of scattered light was determined. It was found that the degree of polarization of the RS is related to the size of the nanocrystals in the samples. An array of nanocrystals with the same crystallographic orientation was obtained by thermal annealing of a silicon single crystal damaged by ion implantation. During thermal annealing of the sample, the crystallinity of the layer is restored not simultaneously in the entire damaged volume, but in the form of nanocrystals separated by amorphous area. All the clusters formed have the same crystallographic orientation of the original single crystal. The features of the degree of polarization of the RS in nanocrystals are associated with the quantum-mechanical uncertainty of the phonon wave vector and the uncertainty of the phonon direction in a limited volume of the nanocrystal. The relations linking the degree of polarization of the RS with the size of nanocrystals are obtained. A technique for determining the size of nanocrystals by measuring the degree of polarization of the RS is discussed. Keywords: Raman scattering of light, silicon, nanocrystals, ion implantation, annealing, amorphous phase.