  We constrain the rotational kinematic Sunyaev-Zel'dovich (rkSZ) effect in
Planck data using a sample of rotating galaxy clusters identified in the Sloan
Digital Sky Survey (SDSS). We extract cluster-centered cutouts from Planck
cosmic microwave background (CMB) maps that have been cleaned of thermal SZ
signal. Using previous constraints on the cluster rotation vectors determined
from the motions of galaxies, we fit for the amplitude of the rkSZ effect in
the CMB cutouts, marginalizing over parameters describing the cluster electron
distribution. We also employ an alternative, less model-dependent approach to
measuring the rkSZ signal that involves measuring the dipole induced by the
rkSZ in rotation velocity-oriented CMB stacks. In both cases, we find roughly
$2\sigma$ evidence for a rkSZ signal consistent with the expected amplitude and
morphology. We comment on future directions for measurements of the rkSZ
signal.
