We present a cosmic microwave background (CMB) lensing map produced from a linear combination of South Pole Telescope (SPT) and Planck temperature data. The 150 GHz temperature data from the 2500 deg2 SPT-SZ survey is combined with the Planck 143 GHz data in harmonic space to obtain a temperature map that has a broader ℓ coverage and less noise than either individual map. Using a quadratic estimator technique on this combined temperature map, we produce a map of the gravitational lensing potential projected along the line of sight. We measure the auto-spectrum of the lensing potential CLφφ, and compare it to the theoretical prediction for a ΛCDM cosmology consistent with the Planck 2015 data set, finding a best-fit amplitude of 0.95-0.06+0.06(stat.)0.01+0.01(sys.). The null hypothesis of no lensing is rejected at a significance of 24σ. One important use of such a lensing potential map is in cross-correlations with other dark matter tracers. We demonstrate this cross-correlation in practice by calculating the cross-spectrum, CLφG, between the SPT+Planck lensing map and Wide-field Infrared Survey Explorer (WISE) galaxies. We fit CLφG to a power law of the form PL = a(L/L0)-b with a, L 0, and b fixed, and find ηφG = CLφG/PL = 0.94-0.04+0.04, which is marginally lower, but in good agreement with ηφG = 1.00-0.01+0.02, the best-fit amplitude for the cross-correlation of Planck-2015 CMB lensing and WISE galaxies over ∼67% of the sky. The lensing potential map presented here will be used for cross-correlation studies with the Dark Energy Survey, whose footprint nearly completely covers the SPT 2500 deg2 field.