We present an experimental technique to generate partially coherent vortex beams with an arbitrary azimuthal index using only a spatial light modulator. Our approach is based on digitally simulating the intrinsic randomness of broadband light passing through a spiral phase plate. We illustrate the versatility of the technique by generating partially coherent beams with different coherence lengths and orbital angular momentum content, without any moving optical device. Consequently, we study its cross-correlation function in a wavefront folding interferometer. The comparison with theoretical predictions yields excellent agreement.