In polarimetric radars, corresponding to the polarized antennas, exploiting waveform diversity along the polarization dimension becomes accessible. In this article, we aim to maximize the signal-to-interference plus noise ratio (SINR) of a polarimetric radar by optimizing the transmit polarimetric waveform, the power allocation on its horizontal and vertical polarization segments, and the receiving filters jointly, subject to separate (while practical) unit-modulus and similarity constraints. To mitigate the SINR sensitivity on Target-Aspect-Angle (TAA), the average Target-Impulse-Response Matrix (TIRM) within a certain (TAA) interval is employed as the target response, which leads to an average SINR as the metric to be maximized. For the formulated nonconvex fractional programming problem, we propose an efficient algorithm under the framework of the alternating optimization method. Within, the alternating direction method of multiplier (ADMM) is deployed to solve the inner subproblems with closed form solutions obtained at each iteration. The analysis on computational cost and convergence of the proposed algorithm is also provided. Experiment results show the effectiveness of the proposed algorithm, the robustness of the output SINR against the TAA uncertainty, and the superior performance of polarimetric power adaption.