In this work, the tunable properties of nematic liquid crystals are exploited in order to design a Fabry-Perot cavity (FPC) leaky-wave antenna (LWA) with beam steering capability at fixed frequency in the THz range. The considered design is a grounded dielectric slab covered with a multistack of alternating layers of low- and high-permittivity dielectric materials, consisting of nematic liquid crystals and alumina thin films, respectively. The former allows for achieving the beam-steering capability at a fixed frequency. Full-wave simulations confirmed the pattern reconfigurability of the device, thus opening very interesting possibilities for the realization of reconfigurable THz antennas.