A low-cost millimeter-wave circularly polarized (CP) planar integrated magneto-electric dipole (ME-dipole) element with simple structure is proposed, which is fed by a low-profile feeding structure capable of being directly integrated with Ka-band front-end circuits. Two rotationally symmetrical L-shaped patches are adopted to replace the two straight arms of the original linearly polarized ME-dipole to generate a rotated electric field, thus radiating CP waves. Based on this CP ME-dipole element, CP array antennas containing 2 x 2 and 4 x 4 radiators with low-profile full-corporate feeding networks are developed without any additional dielectric layer. Prototypes of these two CP array antennas are fabricated and measured. Good agreement between the simulated and measured results is achieved, validating the correctness of these two designs. The 2 x 2 array exhibits a |S-11| < -10 dB relative bandwidth of 34.67%, a 3 dB axial-ratio bandwidth of 11.33%, and a maximum gain of 13.12 dBic, while the corresponding performance of the 4 x 4 array is 21.83%, 5.9%, and 18.28 dBic, respectively. Thus, they can be good candidates for applications, for example, 5G millimeter-wave communications, Ka-band satellite communications, etc.