  The DMASS sample is a photometric sample from the DES Year 1 data set
designed to replicate the properties of the CMASS sample from BOSS, in support
of a joint analysis of DES and BOSS beyond the small overlapping area. In this
paper, we present the measurement of galaxy-galaxy lensing using the DMASS
sample as gravitational lenses in the DES Y1 imaging data. We test a number of
potential systematics that can bias the galaxy-galaxy lensing signal, including
those from shear estimation, photometric redshifts, and observing conditions.
After careful systematic tests, we obtain a highly significant detection of the
galaxy-galaxy lensing signal, with total $S/N=25.7$. With the measured signal,
we assess the feasibility of using DMASS as gravitational lenses equivalent to
CMASS, by estimating the galaxy-matter cross-correlation coefficient $r_{\rm
cc}$. By jointly fitting the galaxy-galaxy lensing measurement with the galaxy
clustering measurement from CMASS, we obtain $r_{\rm cc}=1.09^{+0.12}_{-0.11}$
for the scale cut of $4~h^{-1}{\rm Mpc}$ and $r_{\rm cc}=1.06^{+0.13}_{-0.12}$
for $12~h^{-1}{\rm Mpc}$ in fixed cosmology. By adding the angular galaxy
clustering of DMASS, we obtain $r_{\rm cc}=1.06\pm 0.10$ for the scale cut of
$4~h^{-1}{\rm Mpc}$ and $r_{\rm cc}=1.03\pm 0.11$ for $12~h^{-1}{\rm Mpc}$. The
resulting values of $r_{\rm cc}$ indicate that the lensing signal of DMASS is
equivalent to the one that would have been measured if CMASS had populated the
DES region within the given statistical uncertainty. The measurement of
galaxy-galaxy lensing presented in this paper will serve as part of the data
vector for the forthcoming cosmology analysis in preparation.
