  We cross-correlate galaxy weak lensing measurements from the Dark Energy
Survey (DES) year-one (Y1) 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 reject the hypothesis of no lensing
with a significance of $10.8\sigma$. When employing angular scale cuts, this
significance is reduced to $6.8\sigma$, which remains the highest
signal-to-noise measurement of its kind to date. We fit the amplitude of the
correlation functions while fixing the cosmological parameters to a fiducial
$\Lambda$CDM model, finding $A = 0.99 \pm 0.17$. 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 $\Omega_{\rm m}=0.261^{+0.070}_{-0.051}$ and
$S_{8}\equiv \sigma_{8}\sqrt{\Omega_{\rm m}/0.3} = 0.660^{+0.085}_{-0.100}$.
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.
