We present the discovery and characterization of a giant planet orbiting the young Sun-like star Kepler-63 (KOI-63, $m_{rm Kp} = 11.6$, $T_{rm eff} = 5576$ K, $M_star = 0.98, M_odot$). The planet transits every 9.43 days, with apparent depth variations and brightening anomalies caused by large starspots. The planets radius is $6.1 pm 0.2 R_{earth}$, based on the transit light curve and the estimated stellar parameters. The planets 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 we can place a rough upper bound of $120 M_{earth}$ (3$sigma$). The host star has a high obliquity ($psi$ = $104^{circ}$), 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.