We present Doppler tomographic observations of the transiting planet Kepler-13b (aka KOI-13b), a highly inflated hot Jupiter orbiting the Teff=8500 K primary of a hierarchical triple stellar system. As the planet transits the rapidly rotating host star, it successively blocks regions of the stellar disk with different radial velocities, causing a “bump” in the stellar spectral line shape, which we resolve spectroscopically. The manner in which this perturbation moves across the stellar line during the transit gives information on the relative alignment between the stellar spin and planetary orbital angular momentum vectors. This is a powerful statistical probe of planetary migration processes, as the expected spin-orbit misalignment distributions from dynamically cold migration (disk interactions) and dynamically hot migration (planet-planet scattering, Kozai cycles) are significantly different: the former will lead to primarily aligned orbits; the latter to a wide distribution. Doppler tomography also promises to be a powerful technique for confirming transiting planet candidates around rapidly rotating stars like Kepler-13A, which are not amenable to radial velocity follow-up and thus are currently a poorly sampled region of parameter space.