  We measure the cosmic shear power spectrum on large angular scales by
cross-correlating the shapes of ~9 million galaxies measured in the optical
SDSS survey with the shapes of ~2.7x10^5 radio galaxies measured by the
overlapping VLA-FIRST survey. Our measurements span the multipole range 10 < l
< 130, corresponding to angular scales 2deg < {\theta} < 20deg. On these
scales, the shear maps from both surveys suffer from significant systematic
effects that prohibit a measurement of the shear power spectrum from either
survey alone. Conversely we demonstrate that a power spectrum measured by
cross-correlating the two surveys is unbiased.
  We measure an E-mode power spectrum from the data that is inconsistent with
zero signal at the 99\% confidence (~2.7{\sigma}) level. The odd-parity B-mode
signal and the EB cross- correlation are both found to be consistent with zero
(within 1{\sigma}). These constraints are obtained after a careful error
analysis that accounts for uncertainties due to cosmic variance, random galaxy
shape noise and shape measurement errors, as well as additional errors
associated with the observed large-scale systematic effects in the two surveys.
Our constraints are consistent with the expected signal in the concordance
cosmological model assuming recent estimates of the cosmological parameters
from the Planck satellite, and literature values for the median redshifts of
the SDSS and FIRST galaxy populations.
  The cross-power spectrum approach described in this paper represents a
powerful technique for mitigating shear systematics and will be ideal for
extracting robust results, with the exquisite control of systematics required,
from future cosmic shear surveys with the SKA, LSST, Euclid and WFIRST-AFTA.
