A high-gain reflectarray antenna is proposed with dual-linear to dual-circular polarization conversion for small satellite missions in Ka-band. The reflectarray antenna consists of 42 × 42 reflectarray cells based on two orthogonal and stacked sets of three parallel dipoles. The unit-cell has been characterized to provide a suitable in-band performance. The polarizer reflectarray antenna has been designed cell by cell considering the real angles of incidence on each cell. The simulated radiation patterns show a remarkable operation, with less than 0.2 dB of losses due to the phase errors occurred during the design process and the dielectric losses at 28 GHz. The simulations show a highly satisfactory in-band operation, with at least a 2 GHz bandwidth with an axial ratio lower than 1.5 dB.