  We study the ellipticity of galaxy cluster halos as characterized by the
distribution of cluster galaxies and as measured with weak lensing. We use
monte-carlo simulations of elliptical cluster density profiles to estimate and
correct for Poisson noise bias, edge bias and projection effects. We apply our
methodology to 10,428 SDSS clusters identified by the redMaPPer algorithm with
richness above 20. We find a mean ellipticity $= 0.271 \pm 0.002$ (stat) $\pm
0.031$ (sys) corresponding to an axis ratio $= 0.573 \pm 0.002$ (stat) $\pm
0.039$ (sys). We compare this ellipticity of the satellites to the halo shape,
through a stacked lensing measurement using optimal estimators of the lensing
quadrupole based on Clampitt and Jain (2016). We find a best-fit axis ratio of
$0.56 \pm 0.09$ (stat) $\pm 0.03$ (sys), consistent with the ellipticity of the
satellite distribution. Thus cluster galaxies trace the shape of the dark
matter halo to within our estimated uncertainties. Finally, we restack the
satellite and lensing ellipticity measurements along the major axis of the
cluster central galaxy's light distribution. From the lensing measurements we
infer a misalignment angle with an RMS of ${30^\circ \pm 10}^\circ$ when
stacking on the central galaxy. We discuss applications of halo shape
measurements to test the effects of the baryonic gas and AGN feedback, as well
as dark matter and gravity. The major improvements in signal-to-noise expected
with the ongoing Dark Energy Survey and future surveys from LSST, Euclid and
WFIRST will make halo shapes a useful probe of these effects.
