Automotive radar is an important sensor technology for self-driving cars and Advanced Driver-Assistance Systems (ADAS). Current automotive radars lack the ability to classify and categorize objects due to their limited angular resolution. A new generation of automotive radar systems, known as automotive imaging radars, proposes to overcome this limitation by using larger apertures with more antenna elements. During the radar operation, automotive imaging radar systems face challenges in the accurate estimation of the Direction-of-Arrival (DoA) due to phase incoherency in the spatially sampled information caused by hardware imperfections, temperature variations, and aging effects. This work proposes a method combining convex optimization and alternating updates to first jointly calibrate the phase incoherencies and estimate the DoAs, and then update them iteratively. It further derives the Cramér-Rao Bound (CRB) and investigates the impact of the phase incoherency on DoA estimation using the CRB. In the proposed approach, the MUltiple SIgnal Classification (MUSIC) algorithm is applied to estimate the DoAs after each calibration. Additionally, the eigenvalue decomposition process in MUSIC is replaced by the Projection Approximation Subspace Tracking (PAST) algorithm to reduce computational complexity while maintaining the accuracy of DoA estimation. Experimental results illustrate the effectiveness of these techniques, highlighting their potential in improving next-generation automotive radar systems.