In this communication we propose the concept of a circularly polarized reflectarray (RA) antenna capable of independent beam-switching in both K and Ka bands. The RA unit cell comprises one microstrip ring per each operation frequency. Each ring is integrated with six equally spaced series RF micro electro-mechanical systems (RF MEMS) switches, which allows implementing the sequential rotation principle formerly used in circularly-polarized RA for single-frequency operation. A detailed design is proposed, considering the best relative arrangement of the rings corresponding to each frequency, the accurate modeling of the RF MEMS switches, and the full-wave simulation of the full array. The designed RA is implemented on a 4-inch quartz wafer and comprises 109 K-band and 124 Ka-band split-rings. Two prototypes representing two frozen states of the reconfigurable antenna are fabricated and measured. The designed RA can +/- 120 degrees provide progressive phase difference in both operation bands exhibiting beam switching to +/- 35 degrees and +/- 24 degrees off the broad-side in K and Ka bands respectively. The performance of the designed antenna is verified by the agreement of the measured and simulated radiation patterns.