Terahertz (THz) band is envisioned for the future sixth generation wireless systems thanks to its abundant bandwidth and very narrow beamwidth. These features are one of the key enabling factors for high resolution sensing with milli-degree level direction-of-arrival (DOA) estimation. Therefore, this paper investigates the DOA estimation problem in THz systems in the presence of two major error sources: 1) gain-phase mismatches, which occur due to the deviations in the radio-frequency circuitry; 2) beam-squint, which is caused because of the deviations in the generated beams at different subcarriers due to ultra-wide bandwidth. An auto-calibration approach, namely NoisE subspAce correcTion technique for MUltiple SIgnal Classification (NEAT-MUSIC), is proposed based on the correction of the noise subspace for accurate DOA estimation in the presence of gain-phase mismatches and beam-squint. To gauge the performance of the proposed approach, the Cramer-Rao bounds are also derived. Numerical results show the effectiveness of the proposed approach.