A white dwarf (WD) approaching the Chandrasekhar mass may in several cases undergo accretion-induced collapse (AIC) to a neutron star (NS) before a thermonuclear explosion ensues. It has generally been assumed that AIC does not produce a detectable supernova (SN). If, however, the progenitor WD is rapidly rotating (as may be expected due to its prior accretion), a centrifugally supported disk forms around the NS upon collapse. We calculate the subsequent evolution of this accretion disk using time-dependent height-integrated simulations with initial conditions taken from the AIC calculations of Dessart et al. (2006). Initially, the disk is cooled by neutrinos and its composition is driven neutron-rich (electron fraction Ye ~ 0.1) by electron captures. However, as the disk viscously spreads, it is irradiated by neutrinos from the central proto-NS, which dramatically alters its neutron-to-proton ratio. We find that electron neutrino captures increase Ye to ~ 0.5 by the time that weak interactions in the disk freeze out. Because the disk becomes radiatively inefficient and begins forming alpha-particles soon after freeze out, powerful winds blow away most of the disks remaining mass. These Ye ~ 0.5 outflows synthesize up to a few times 1e-2 Msun in 56Ni. As a result, AIC may be accompanied by a radioactively powered SN-like transient that peaks on a timescale of ~ 1 day. Since few intermediate mass elements are likely synthesized, these Ni-rich explosions should be spectroscopically distinct from other SNe. PanSTARRs and the Palomar Transient Factory should detect a few AIC transients per year if their true rate is ~1/100 of the Type Ia rate, and LSST should detect hundreds per year. High cadence observations (< 1 day) are optimal for the detection and follow-up of AIC (abridged).