We present a new single-shot, full-Stokes optical astro-polarimeter design using stress-engineered optics (SEOs). The SEO is a cylindrical glass window under static stress by radially-inward forces in three symmetrically-space regions, producing spatially-varying birefringence throughout (Spilman and Brown, Applied Optics IP, 46, 2007), and can be produced by using o-the-shelf supplies and some machining. By collimating light collected by a telescope through the SEO and then focusing it onto a detector, the system's point spread function (PSF) acquires a shape uniquely dependent on the full polarization vector of the input light (Beckley and Brown, Proc. SPIE, 757011, 2010). By measuring the imaged PSFs, the full-Stokes polarization states of all point sources (stars) in the field can ideally be determined from a single exposure and without division of amplitude techniques. Prior to our instrument, these techniques and technology had not yet been applied to astronomy. Aside from filter wheels and focusing elements, our instrument contains no moving parts. The instrument will operate by first taking a set of calibration exposures of 100% polarized light using swap-in polarizers in one of its filter wheels. Once the calibration images are taken, the polarizers are removed form the light path, and the science target (star) is imaged. Using techniques described in this paper, the calibration images allow one to determine the unknown polarization of the science target. This process is repeated in multiple photometric bands at visible wavelengths for color-dependent studies. The successful application of this polarimeter technology in astronomy would mark a step forward for increasing polarimetry efficiency (no temporal modulation required) and simplicity of instrumentation (no spatial modulation required). Contained in this paper are the on-sky commissioning results of our polarimeter on an 0:2m (8in) telescope at the University of Denver, and an in-depth look at the effect of Earth's atmospheric turbulence on the polarization-dependent PSF detection. We have also begun testing the instrument's capabilities in measuring both linear and circular interstellar polarization, and a look at the variability of historic polarized and unpolarized "standard" stars. Better understanding of the interstellar component of the polarization of stars and the nature of calibration stars are required for all future polarimetric measurements. The authors are grateful to the estate of William Herschel Womble for the support of astronomy at the University of Denver.