One of the most ambitious projects in communications in recent years is the development of the so-called satellite mega-constellations. Comprised of hundreds or thousands of small and low-cost satellites, they aim to provide internet services in places without existing broadband access. For the antenna subsystem, reflectarrays have been proposed as a cheap solution due to their low profile and manufacturing costs, while still providing good performance. This paper presents a full design of a reflectarray antenna for mega-constellation satellites with a shaped-beam isoflux pattern for constant power flux in the surface of the Earth. A unit cell consisting of two stacked rectangular microstrip patches backed by a ground plane is employed, providing more than 360° of phase-shift. The generalized intersection approach optimization algorithm is employed to synthesize the required isoflux pattern in a 2 GHz bandwidth in Ku-band. To that purpose, a full-wave electromagnetic analysis is employed for the wideband design. The optimized reflectarray layout complies with the specifications of the isoflux pattern in the frequency band 16 GHz-18 GHz, demonstrating the capabilities of this type of antenna to provide a low-cost, low-profile solution for the user beam segment, including different types of shaped beams.