We place constraints on the matter density of the Universe and the amplitude of clustering using measurements of the galaxy two-point correlation function from the Sloan Digital Sky Survey (SDSS). We generate model predictions for different cosmologies by populating rescaled N-body simulations with galaxies using the subhalo abundance matching (SHAM) technique. We find Omega-M = 0.29 +/- 0.03 and sigma-8 = 0.86 +/- 0.04 at 68% confidence from fitting the observed two-point galaxy correlation function of galaxies brighter than M_r = -18 in a volume limited sample of galaxies obtained by the SDSS. We discuss and quantify potential sources of systematic error, and conclude that while there is scope for improving its robustness, the technique presented in this paper provides a powerful low redshift constraint on the cosmological parameters that is complementary to other commonly used methods.