We demonstrate numerically and experimentally that, in vertical-cavity surface-emitting lasers (VCSELs), a non-chiral cavity can be converted into a chiral one by the interaction between a sub-wavelength grating tilted with respect to the crystalline axes and the intrinsic semiconductor optical anisotropies, thus enabling the emission of elliptically polarized light. The measured Stokes parameters of such a VCSEL, realized by a standard grating based VCSEL fabricati on process, are in line with the modeling results. We demonstrate through simulations that a degree of circular polarization of 0.9 can be obtained by varying the grating parameters. The full Poincaré sphere is accessible on demand if mechanical strain is also considered.