Conventional sensing applications rely on electromagnetic far-field channel models with plane wave propagation. However, recent ultra-short-range automotive radar applications at upper millimeter-wave or low terahertz (THz) frequencies envisage operation in the near-field region, where the wavefront is spherical. Unlike far-field, the near-field beampattern is dependent on both range and angle, thus requiring a different approach to waveform design. For the first time in the literature, we adopt the beampattern matching approach to design unimodular waveforms for THz automotive radars with low weighted integrated sidelobe levels (WISL). We formulate this problem as a unimodular bi-quadratic matrix program, and solve its constituent quadratic sub-problems using our cyclic power method-like iterations (CyPMLI) algorithm. Numerical experiments demonstrate that the CyPMLI approach yields the required beampattern with low autocorrelation levels.