Beam-scanning capabilities for space-borne sub- millimeter-wave spectrometers are critical for instrument calibration and field-of-view mapping. However, the lack of low-loss waveguide-integrated phase shifters above 500 GHz has been a significant challenge for realizing Terahertz phased array antennas. Recently developed microelectromechanical system (MEMS)actuated phase shifters have emerged as promising candidates, initially demonstrating a 145 degrees phase shift. As a first demonstration of the efficacy of these phase shifters for electronic beam- steering, we present the design, fabrication, and characterization of a linear, near-Nyquist sampled, 4 x 1-element phased array operating from 500 to 600 GHz. The array element is a silicon micromachined leaky-wave feed based on a Fabry-Perot cavity to enhance directivity and reduce grating lobes while achieving bandwidth requirements with minimal scan loss. It is shown, through measurements, that this antenna feed is suitable for use in larger 8 x 1-element arrays for applications that require moderate gain (20 dBi) and scanning (+/- 20 degrees) with a fan beam. Furthermore, we present measurement results of a second generation of MEMS phase shifters with an increased measured phase shift up to 350 degrees. A full 360 degrees phase-wrapping capability is desired as this will enable high-gain lens-scanning phased arrays that can be used for future submillimeter-wave spectrometers.