On 13 December 2006 the IceTop air shower array at the South Pole detected a major solar particle event. By numerically simulating the response of the IceTop tanks, which are thick Cherenkov detectors with multiple thresholds deployed at high altitude with no geomagnetic cut-off, we determined the particle energy spectrum in the energy range 0.6 to 7.6 GeV. This is the first such spectral measurement using a single instrument with a well defined viewing direction. We compare the IceTop spectrum and its time evolution with previously published results and outline plans for improved resolution of future solar particle spectra.