We present a measurement of the angular power spectrum of the cosmic microwave background ( CMB ) using data from the South Pole Telescope ( SPT ) . The data consist of 790 square degrees of sky observed at 150 GHz during 2008 and 2009 . Here we present the power spectrum over the multipole range 650 < \ell < 3000 , where it is dominated by primary CMB anisotropy . We combine this power spectrum with the power spectra from the seven-year Wilkinson Microwave Anisotropy Probe ( WMAP ) data release to constrain cosmological models . We find that the SPT and WMAP data are consistent with each other and , when combined , are well fit by a spatially flat , \Lambda CDM cosmological model . The SPT+WMAP constraint on the spectral index of scalar fluctuations is n _ { s } = 0.9663 \pm 0.0112 . We detect , at \sim 5 \sigma significance , the effect of gravitational lensing on the CMB power spectrum , and find its amplitude to be consistent with the \Lambda CDM cosmological model . We explore a number of extensions beyond the \Lambda CDM model . Each extension is tested independently , although there are degeneracies between some of the extension parameters . We constrain the tensor-to-scalar ratio to be r < 0.21 ( 95 % CL ) and constrain the running of the scalar spectral index to be dn _ { s } / d \ln k = -0.024 \pm 0.013 . We strongly detect the effects of primordial helium and neutrinos on the CMB ; a model without helium is rejected at 7.7 \sigma , while a model without neutrinos is rejected at 7.5 \sigma . The primordial helium abundance is measured to be Y _ { p } = 0.296 \pm 0.030 , and the effective number of relativistic species is measured to be N _ { \mathrm { eff } } = 3.85 \pm 0.62 . The constraints on these models are strengthened when the CMB data are combined with measurements of the Hubble constant and the baryon acoustic oscillation feature . Notable improvements include n _ { s } = 0.9668 \pm 0.0093 , r < 0.17 ( 95 % CL ) , and N _ { \mathrm { eff } } = 3.86 \pm 0.42 . The SPT+WMAP data show a mild preference for low power in the CMB damping tail , and while this preference may be accommodated by models that have a negative spectral running , a high primordial helium abundance , or a high effective number of relativistic species , such models are disfavored by the abundance of low-redshift galaxy clusters .