We report constraints on cosmological parameters from the angular power spectrum of a cosmic microwave background (CMB) gravitational lensing potential map created using temperature data from 2500 deg2 of South Pole Telescope (SPT) data supplemented with data from Planck in the same sky region, with the statistical power in the combined map primarily from the SPT data. We fit the lensing power spectrum to a model including cold dark matter and a cosmological constant ( ), and to models with single-parameter extensions to . We find constraints that are comparable to and consistent with those found using the full-sky Planck CMB lensing data, e.g., = 0.598 0.024 from the lensing data alone with weak priors placed on other parameters. Combining with primary CMB data, we explore single-parameter extensions to . We find or < 0.70 eV at 95% confidence, in good agreement with results including the lensing potential as measured by Planck. We include two parameters that scale the effect of lensing on the CMB: , which scales the lensing power spectrum in both the lens reconstruction power and in the smearing of the acoustic peaks, and , which scales only the amplitude of the lensing reconstruction power spectrum. We find × = 1.01 0.08 for the lensing map made from combined SPT and Planck data, indicating that the amount of lensing is in excellent agreement with expectations from the observed CMB angular power spectrum when not including the information from smearing of the acoustic peaks.