Far-field slit diffraction of circular optical-vortex (OV) beams is efficient for measurement of the topological charge (TC) magnitude but does not reveal its sign. We show that this is because in the common diffraction schemes the diffraction plane coincides with the incident OV waist plane. Based on the examples of Laguerre-Gaussian incident beams containing a spherical wavefront component, we demonstrate that the far-field diffracted beam profile possesses an asymmetry depending on the incident wavefront curvature and the TC sign. This finding enables simple and efficient ways for the simultaneous diagnostics of the TC magnitude and sign, which can be useful in many OV applications, including OV-assisted metrology and information processing.