  We perform an Alcock-Paczynski test using stacked cosmic voids identified in
the SDSS Data Release 7 main sample and Data Release 10 LOWZ and CMASS samples.
We find ~1,500 voids out to redshift $0.6$ using a heavily modified and
extended version of the watershed algorithm ZOBOV, which we call VIDE (Void
IDentification and Examination). To assess the impact of peculiar velocities we
use the mock void catalogs presented in Sutter et al. (2013). We find a
constant uniform flattening of 14% along the line of sight when peculiar
velocities are included. This flattening appears universal for all void sizes
at all redshifts and for all tracer densities. We also use these mocks to
identify an optimal stacking strategy. After correcting for systematic effects
we find that our Alcock-Paczynski measurement leads to a preference of our
best-fit value of $\Omega_{\rm M}\sim 0.15$ over $\Omega_{\rm M} = 1.0$ by a
likelihood ratio of 10. Likewise, we find a factor of $4.5$ preference of the
likelihood ratio for a $\Lambda$CDM $\Omega_{\rm M} = 0.3$ model and a null
measurement. Taken together, we find substantial evidence for the
Alcock-Paczynski signal in our sample of cosmic voids. Our assessment using
realistic mocks suggests that measurements with future SDSS releases and other
surveys will provide tighter cosmological parameter constraints. The
void-finding algorithm and catalogs used in this work will be made publicly
available at http://www.cosmicvoids.net.
