This paper presents a novel frequency reconfigurable phase shifter using the RF microelectromechanical systems (MEMS) technology. The phase shifter is based on the triple-stub circuit topology composed of three stubs that are connected by two transmission lines that are all implemented as distributed MEMS transmission lines. The insertion phase of the circuit is controlled by changing the electrical lengths of the stubs and the connecting transmission lines, while having ideally zero reflection coefficient at all times. The phase shifter has theoretically no specific limits on the frequency; in other words, it can be reconfigured to work at any frequency between 15-40 GHz, with adjustable phase steps, while providing a constant time delay within a 2%-3% instantaneous bandwidth around any selected center frequency in the above-mentioned band. The phase shifter is fabricated monolithically using a surface micromachining process on a quartz substrate and occupies 10.8 mm x 5.9 mm. Measurement results show that the phase shifter has average phase error of 1.6 degrees, 3.7 degrees, and 4.7 degrees, average insertion loss of 3.1, 5, and 8.2 dB and average return loss of 19.3, 15.8, and 13.7 dB at 15, 30, and 40 GHz, respectively. To the best of our knowledge, this paper demonstrates the first phase shifter in the literature that can work at any given frequency in a targeted band with adjustable phase steps.