We cross-correlate galaxy weak lensing measurements from the Dark Energy Survey (DES) year-one data with a cosmic microwave background (CMB) weak lensing map derived from South Pole Telescope (SPT) and Planck data, with an effective overlapping area of 1289 deg(2). With the combined measurements from four source galaxy redshift bins, we obtain a detection significance of 5.8 sigma. We fit the amplitude of the correlation functions while fixing the cosmological parameters to a fiducial Lambda CDM model, finding A = 0.99 +/- 0.17. We additionally use the correlation function measurements to constrain shear calibration bias, obtaining constraints that are consistent with previous DES analyses. Finally, when performing a cosmological analysis under the Lambda CDM model, we obtain the marginalized constraints of Omega(m) = 0.261(-0.051)(+0.070) and S-8 = sigma(8)root Omega(m)/0.3 = 0.660(-0.100)(+0.085). These measurements are used in a companion work that presents cosmological constraints from the joint analysis of two-point functions among galaxies, galaxy shears, and CMB lensing using DES, SPT, and Planck data.