In this work, the design of array antennas for producing dual-circularly-polarized dual-beam radiation via element rotation and phasing is presented. In the pattern synthesis of an antenna array, by exploiting both radiator rotation and phased feeding for all the array elements, the beamforming for left- and right-handed circularly-polarized (LHCP and RHCP) radiated waves can be independent controlled, thus resulting in dual-circularly-polarized high-gain beams each pointing at an arbitrary direction. To verify the proposed technique, a linear array with 16-elements and a planar array containing 4×4 elements are designed and simulated. The proposed antenna arrays have a simple structure, a wide bandwidth, and high polarization purity.