In this paper, we propose a new design concept of a beam-steerable, two-element array of microstrip patch antennas for 5G smartphone applications. The main beam is steered toward different directions through the use of a tunable phase shifter based on nematic liquid crystals (N-LC). The relative phase introduced at the input terminals of the two patch antennas is controlled through a bias voltage between 0 and 10 Volts. This external bias voltage changes the orientation of the LC molecules inside a cavity underneath the microstrip line, thus affecting the dielectric constant of the material, and effectively, the time delay. The antennas are fed through a feed network of microstrip lines. This design was optimized to provide impedance matching and low reflection coefficient. Simulation results using ANSYS HFSS reveal that the main beam can be switched toward different directions through the use of a low-intensity, low-frequency AC voltage that is applied externally between the microstrip line of the phase shifter and the common ground.