The shape of the angular power spectrum of galaxies in the linear regime is defined by the horizon size at the matter-radiation equality. When calibrated by cosmic microwave background measurements, this shape can be used as a standard ruler to estimate angular diameter distances out to the redshift at which clustering is measured. We apply this cosmological test to a recent set of angular clustering spectra from the Sloan Digital Sky Survey. We measure comoving angular diameter distances with a fractional accuracy of around 15%-20% out to eight redshift bins between redshifts of 0.2 and 0.6 after marginalizing over the bias factors and cosmological parameters that define the primordial matter power spectrum. Using clustering measurements out to a multipole of 150 in each of the bins and using a nonlinear correction to the power spectrum, the derived Hubble constant is 69 km s^-1 Mpc^-1 at the 68% confidence level. A 3% lower Hubble constant is recovered if measurements are restricted only to the linear region with k < 0.1 h Mpc^-1. We comment on the expected improvements with future surveys.