  We present galaxy-galaxy lensing results from 139 square degrees of Dark
Energy Survey (DES) Science Verification (SV) data. Our lens sample consists of
red galaxies, known as redMaGiC, which are specifically selected to have a low
photometric redshift error and outlier rate. The lensing measurement has a
total signal-to-noise of 29 over scales $0.09 < R < 15$ Mpc/$h$, including all
lenses over a wide redshift range $0.2 < z < 0.8$. Dividing the lenses into
three redshift bins for this constant moving number density sample, we find no
evidence for evolution in the halo mass with redshift. We obtain consistent
results for the lensing measurement with two independent shear pipelines, ngmix
and im3shape. We perform a number of null tests on the shear and photometric
redshift catalogs and quantify resulting systematic uncertainties. Covariances
from jackknife subsamples of the data are validated with a suite of 50 mock
surveys. The results and systematics checks in this work provide a critical
input for future cosmological and galaxy evolution studies with the DES data
and redMaGiC galaxy samples. We fit a Halo Occupation Distribution (HOD) model,
and demonstrate that our data constrains the mean halo mass of the lens
galaxies, despite strong degeneracies between individual HOD parameters.
