This paper proposes an extended prism coupling analysis method to accurately analyze the coupling structure of liquid crystal (LC) cladding waveguide beam steerer. We analyze the effects of LC anisotropy on the coupling of transverse electric (TE) and transverse magnetic (TM) modes and derive the expression of the optical field distribution that perfectly matches the given coupling structure. Based on this method, we present the optimal coupling structure for Gaussian beam. Taking into account the practical manufacturing process, we propose a simplified coupling structure and perform a detailed analysis of its performance based on numerical simulations. Experimental results show a coupling efficiency of 91% and a coupling angle full width at half maximum (FWHM) of about ±0.02°, demonstrating the effectiveness of the proposed method in predicting the coupling performance of anisotropic cladding waveguides.