The increasing demand for ultra-high data rates in wireless communications has attracted interest in upper-frequency bands, namely sub-terahertz and terahertz frequencies. However, severe path loss and narrow beamwidth antennas used at these frequencies necessitate precise antenna alignment and realignment algorithms. Existing solutions often rely on constrained simulations or out-of-band techniques that may not capture the unique propagation characteristics of terahertz frequencies. To address this challenge, we introduce THzAlign, an integrated sub-terahertz and terahertz platform that enables rapid prototyping and real-world testing of antenna alignment algorithms. THzAlign combines rotary tables for precise beam steering with a modular software architecture supporting algorithm simulation and over-the-air experiments. To illustrate this platform, we evaluate three reference realignment algorithms in terms of their performance using THzAlign under varying distances, frequencies, and antenna beamwidth conditions. The developed platform with its documented API facilitates real-world hardware validation of forthcoming advanced solutions for beam (re-)alignment as an integral part of intelligent ultra-high-rate communication systems in the (sub-)THz bands toward 6G and beyond.