  We derive constraints on the matter density \Om and the amplitude of matter
clustering \sig8 from measurements of large scale weak lensing (projected
separation R=5-30\hmpc) by clusters in the Sloan Digital Sky Survey MaxBCG
catalog. The weak lensing signal is proportional to the product of \Om and the
cluster-mass correlation function \xicm. With the relation between optical
richness and cluster mass constrained by the observed cluster number counts,
the predicted lensing signal increases with increasing \Om or \sig8, with mild
additional dependence on the assumed scatter between richness and mass. The
dependence of the signal on scale and richness partly breaks the degeneracies
among these parameters. We incorporate external priors on the richness-mass
scatter from comparisons to X-ray data and on the shape of the matter power
spectrum from galaxy clustering, and we test our adopted model for \xicm
against N-body simulations. Using a Bayesian approach with minimal restrictive
priors, we find \sig8(\Om/0.325)^{0.501}=0.828 +/- 0.049, with marginalized
constraints of \Om=0.325_{-0.067}^{+0.086} and \sig8=0.828_{-0.097}^{+0.111},
consistent with constraints from other MaxBCG studies that use weak lensing
measurements on small scales (R<=2\hmpc). The (\Om,\sig8) constraint is
consistent with and orthogonal to the one inferred from WMAP CMB data,
reflecting agreement with the structure growth predicted by GR for an LCDM
cosmological model. A joint constraint assuming LCDM yields \Om=0.298 +/- 0.020
and \sig8=0.831 +/- 0.020. Our cosmological parameter errors are dominated by
the statistical uncertainties of the large scale weak lensing measurements,
which should shrink sharply with current and future imaging surveys.
