We present the discovery and characterization of a giant planet orbiting the young Sun-like star Kepler-63 (KOI-63, mKp = 11.6, Teff = 5576 K, Msstarf = 0.98 M⊙). The planet transits every 9.43 days, with apparent depth variations and brightening anomalies caused by large starspots. The planet's radius is 6.1 ± 0.2 R⊕, based on the transit light curve and the estimated stellar parameters. The planet's mass could not be measured with the existing radial-velocity data, due to the high level of stellar activity, but if we assume a circular orbit, then we can place a rough upper bound of 120 M⊕ (3σ). The host star has a high obliquity (ψ = 104°), based on the Rossiter-McLaughlin effect and an analysis of starspot-crossing events. This result is valuable because almost all previous obliquity measurements are for stars with more massive planets and shorter-period orbits. In addition, the polar orbit of the planet combined with an analysis of spot-crossing events reveals a large and persistent polar starspot. Such spots have previously been inferred using Doppler tomography, and predicted in simulations of magnetic activity of young Sun-like stars.