The energy and spectral conditions for single-stage holographic recording of a diffraction optical element based on the carbazole-containing azo polymer, that forms singular light beams (optical vortices), have been established. With the atomic-force microscopy (AFM), the surface morphology of the recorded relief holograms was studying, and their diffraction efficiency has been estimated. The topology of the generated optical phase singularities has been studied and the stability range of an optical vortex having the topological charge l = 2 has been found. The possibility of using the developed diffractive optical element in the scheme of optical tweezers for manipulating micro-objects is demonstrated.