  Kinematic weak lensing describes the distortion of a galaxy's projected
velocity field due to lensing shear, an effect recently reported for the first
time by Gurri et al. based on a sample of 18 galaxies at $z \sim 0.1$. In this
paper, we develop a new formalism that combines the shape information from
imaging surveys with the kinematic information from resolved spectroscopy to
better constrain the lensing distortion of source galaxies and to potentially
address systematic errors that affect conventional weak-lensing analyses. Using
a Bayesian forward model applied to mock galaxy observations, we model
distortions in the source galaxy's velocity field simultaneously with the
apparent shear-induced offset between the kinematic and photometric major axes.
We show that this combination dramatically reduces the statistical uncertainty
on the inferred shear, yielding statistical error gains of a factor of 2--6
compared to kinematics alone. While we have not accounted for errors from
intrinsic kinematic irregularities, our approach opens kinematic lensing
studies to higher redshifts where resolved spectroscopy is more challenging.
For example, we show that ground-based integral-field spectroscopy of
background galaxies at $z \sim 0.7$ can deliver gravitational shear
measurements with S/N $\sim 1$ per source galaxy at 1 arcminute separations
from a galaxy cluster at $z \sim 0.3$. This suggests that even modest samples
observed with existing instruments could deliver improved galaxy cluster mass
measurements and well-sampled probes of their halo mass profiles to large
radii.
