We report the discovery of Kepler-77b (alias KOI-127.01), a Saturn-mass transiting planet in a 3.6-day orbit around a metal-rich solar-like star. We combined the publicly available Kepler photometry (quarters 1-13) with high-resolution spectroscopy from the Sandiford at McDonald and FIES at NOT spectrographs. We derived the system parameters via a simultaneous joint fit to the photometric and radial velocity measurements. Our analysis is based on the Bayesian approach and is carried out by sampling the parameter posterior distributions using a Markov chain Monte Carlo simulation. Kepler-77b is a moderately inflated planet with a mass of Mp = 0.430 ± 0.032 MJup, a radius of Rp = 0.960 ± 0.016 RJup, and a bulk density of ρp = 0.603 ± 0.055 g cm-3. It orbits a slowly rotating (Prot = 36 ± 6 days) G5 V star with M⋆ = 0.95 ± 0.04 M⊙, R⋆ = 0.99 ± 0.02 R⊙, Teff = 5520 ± 60 K, [M/H] = 0.20 ± 0.05 dex, that has an age of 7.5 ± 2.0 Gyr. The lack of detectable planetary occultation with a depth higher than ~10 ppm implies a planet geometric and Bond albedo of Ag ≤ 0.087 ± 0.008 and AB ≤ 0.058 ± 0.006, respectively, placing Kepler-77b among the gas-giant planets with the lowest albedo known so far. We found neither additional planetary transit signals nor transit-timing variations at a level of ~0.5 min, in accordance with the trend that close-in gas giant planets seem to belong to single-planet systems. The 106 transitsobserved in short-cadence mode by Kepler for nearly 1.2 years show no detectable signatures of the planet's passage in front of starspots. We explored the implications of the absence of detectable spot-crossing events for the inclination of the stellar spin-axis, the sky-projected spin-orbit obliquity, and the latitude of magnetically active regions. Based on observations obtained with the 2.1-m Otto Struve telescope at McDonald Observatory, Texas, USA.Based on observations obtained with the Nordic Optical Telescope, operated on the island of La Palma jointly by Denmark, Finland, Iceland, Norway, and Sweden, in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias, in time allocated by OPTICON and the Spanish Time Allocation Committee (CAT).The research leading to these results has received funding from the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement number RG226604 (OPTICON).Appendix A is available in electronic form at http://www.aanda.org