We consider the problem of ESPRIT-oriented precoder design for beamspace angle-of-departure (AoD) estimation in downlink mmWave multiple-input single-output communications. Standard precoders (i.e., directional/sum beams) yield poor performance in AoD estimation, while Cramer-Rao bound-optimized precoders undermine the so-called shift invariance property (SIP) of ESPRIT. To tackle this issue, the problem of designing ESPRIT-oriented precoders is formulated to jointly optimize over the precoding matrix and the SIP-restoring matrix of ESPRIT. We develop an alternating optimization approach that updates these two matrices under unit-modulus constraints for analog beamforming architectures. Simulation results demonstrate the validity of the proposed approach while providing valuable insights on the beampatterns of the ESPRIT-oriented precoders. © 2023 IEEE.