Automotive radar at terahertz (THz) band has the potential to provide compact design. The availability of wide bandwidth at THz-band leads to high range resolution. Further, very narrow beamwidth arising from large arrays yields high angular resolution up to milli-degree level direction-of-arrival (DoA) estimation. At THz frequencies and extremely large arrays, the signal wavefront is spherical in the near-field that renders traditional far-field DoA estimation techniques unusable. In this work, we examine near-field DoA estimation for THz automotive radar. We propose an algorithm using multiple signal classification (MUSIC) to estimate target DoAs and ranges while also taking beam-squint in near-field into account. Using an array transformation approach, we compensate for near-field beam-squint in noise subspace computations to construct the beam-squint-free MUSIC spectra. Numerical experiments show the effectiveness of the proposed method to accurately estimate the target parameters.