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.