  We present weak lensing (WL) mass constraints for a sample of massive galaxy
clusters detected by the South Pole Telescope (SPT) via the Sunyaev-Zeldovich
effect (SZE). We use $griz$ imaging data obtained from the Science Verification
(SV) phase of the Dark Energy Survey (DES) to fit the WL shear signal of 33
clusters in the redshift range $0.25 \le z \le 0.8$ with NFW profiles and to
constrain a four-parameter SPT mass-observable relation. To account for biases
in WL masses, we introduce a WL mass to true mass scaling relation described by
a mean bias and an intrinsic, log-normal scatter. We allow for correlated
scatter within the WL and SZE mass-observable relations and use simulations to
constrain priors on nuisance parameters related to bias and scatter from WL. We
constrain the normalization of the $\zeta-M_{500}$ relation,
$A_\mathrm{SZ}=12.0_{-6.7}^{+2.6}$ when using a prior on the mass slope
$B_\mathrm{SZ}$ from the latest SPT cluster cosmology analysis. Without this
prior, we recover $A_\mathrm{SZ}=10.8_{-5.2}^{+2.3}$ and
$B_\mathrm{SZ}=1.30_{-0.44}^{+0.22}$. Results in both cases imply lower cluster
masses than measured in previous work with and without WL, although the
uncertainties are large. The WL derived value of $B_\mathrm{SZ}$ is $\approx
20\%$ lower than the value preferred by the most recent SPT cluster cosmology
analysis. The method demonstrated in this work is designed to constrain cluster
masses and cosmological parameters simultaneously and will form the basis for
subsequent studies that employ the full SPT cluster sample together with the
DES data.
