We propose a method to distinguish between cloudy, hazy, and clear sky (free of clouds and hazes) exoplanet atmospheres that could be applicable to upcoming large aperture space- and ground-based telescopes such as the James Webb Space Telescope (JWST) and the European Extremely Large Telescope (E-ELT). These facilities will be powerful tools for characterizing transiting exoplanets, but only after a considerable amount of telescope time is devoted to a single planet. A technique that could provide a relatively rapid means of identifying haze-free targets (which may be more valuable targets for characterization) could potentially increase the science return for these telescopes. Our proposed method utilizes broadband observations of refracted light in the out-of-transit spectrum. Light refracted through an exoplanet atmosphere can lead to an increase of flux prior to ingress and subsequent to egress. Because this light is transmitted at pressures greater than those for typical cloud and haze layers, the detection of refracted light could indicate a cloud- or haze-free atmosphere. A detection of refracted light could be accomplished in <10 hr for Jovian exoplanets with JWST and <5 hr for super-Earths/mini-Neptunes with E-ELT. We find that this technique is most effective for planets with equilibrium temperatures between 200 and 500 K, which may include potentially habitable planets. A detection of refracted light for a potentially habitable planet would strongly suggest the planet was free of a global cloud or haze layer, and therefore a promising candidate for follow-up observations.