Context. The study of young solar type stars is fundamental for a better understanding of the magnetic activity of the Sun. Most commonly, this activity manifests itself in the form of spots and faculae. As a planet in transit crosses in front of its host star, a dark spot on the stellar surface may be occulted, causing a detectable variation in the light curve. Kepler-63 is a young solar-like star with an age of only 210 Myr that exhibit photometric variations compatible with spot signatures. Since its orbiting planet is in an almost polar orbit, different latitudes of the star can be probed by the method of spot transit mapping. Aims. The goal of this work is to characterise the spots of Kepler-63 and thus decipher the behaviour of the young Sun. Because of the high obliquity of the planetary orbit, the spots latitudinal distribution and thus its differential rotation may be determined. Methods. A total of 150 transits of Kepler-63b were observed in the short cadence light curve, corresponding to a total duration of about 4 years. Each transit light curve was fit by a model that simulates planetary transits and allows the inclusion of starspots on the surface of the host star. This enables the physical characterisation of the spots size, intensity, and location. We determine the spot position in a reference frame that rotates with the star, and thus obtain the latitudinal distribution of the spots. Results. A total of 297 spots were fit and their sizes, intensities, and positions determined. The spots longitude and latitude were calculated on a reference frame that rotates with the star. The latitude distribution of spots exhibits a bimodality with a lack of spots around 34 • . Moreover, the size of spots tend to be larger close to the equator, decreasing toward the latitude distribution gap, and then increasing again toward the poles. The high latitude spots dominate the magnetic cycle of Kepler-63. For a mean stellar rotation period of 5.400d, 59 spots were found at approximately the same longitude and latitude on a later transit. Some of these spots were detected 8 transits later, showing the existence of spots with lifetimes of at least 75d. Conclusions. Due to the geometry of the Kepler-63 system, we were able to build a starspot "butterfly diagram", similar to that of sunspots. It was also possible to infer Kepler-63 differential rotation from the presence of spots at different latitudes. This star was found to rotate almost rigidly with a period of 5.400d and relative shear close to 0.01% for latitudes less than 34 • , whereas the high latitudes do not follow a well behaved pattern.