A method to detect the photonic topological charges (TCs) of optical vortex beams using a radial phase grating is proposed and demonstrated. The modulus of TCs can be obtained by the number of dark stripes of far-field diffraction patterns, and the sign of TCs is determined by the orientation of the patterns. The detection of TCs up to ±120 is demonstrated with this scheme. In addition, through investigating the evolution of patterns with various azimuthal periods of the grating and the distance between the centers of the grating and vortex beams, we show that this detection scheme has excellent alignment tolerance and does not have stringent requirements on the parameters of the grating.