In this paper, we focus on constant-modulus waveform design for the dual use of radar target detection and cellular transmission. As the MIMO radar typically transmits orthogonal waveforms to search potential targets, we aim at jointly minimizing the downlink multi-user interference and the non-orthogonality of the transmitted waveform. Given the non-convexity in both orthogonal and CM constraints, we decompose the formulated optimization problem as two sub-problems, where we solve one of the sub-problems by singular value decomposition and the other one by the Riemannian conjugate gradient algorithm. We then propose an alternating minimization approach to obtain a near-optimal solution to the original problem by iteratively solve the two sub-problems. Finally, we assess the effectiveness of the proposed approach via numerical simulations.