We investigate the gravitational lensing properties of dark matter halos with Burkert profiles. We derive an analytic expression for the lens equation and use it to compute the magnification, impact parameter, and image separations for strong lensing. For the scaling relation that provides the best fits to spiral galaxy rotation curve data, Burkert halos will not produce strong lensing, even if this scaling relation extends up to masses of galaxy clusters. Tests of a simple model of an exponential stellar disk superposed on a Burkert profile halo demonstrate that strong lensing is unlikely without an additional concentration of mass in the galaxy center (e.g., a bulge). The fact that most strong lenses on galactic scales are elliptical galaxies suggests that a strong central concentration of baryons is required to produce image splitting. This solution is less attractive for clusters of galaxies, which are generally considered to be dark matter dominated even at small radii. There are three possible implications of these results: (1) dark halos may have a variety of inner profiles, (2) dark matter halos may not follow a single scaling relation from galaxy scale up to cluster scale, and/or (3) the splitting of images (even by clusters of galaxies) may in general be due to the central concentration of baryonic material in halos rather than dark matter.