In this paper, we consider the detection problem with the polarization diversity technique in the compound Gaussian sea clutter with Gamma texture. We derive the polarimetric detector based on the maximum a posterior (MAP) and two-step generalized likelihood ratio test (GLRT). In the first step, we assume that the polarimetric clutter covariance matrix (PCCM) and the Gamma textures are known, and we develop the test statistics of the proposed detector. In the second step, we obtain the adaptive polarimetric detector by using the fixed point covariance estimator (FPCE) to estimate the PCCM and the MAP method to estimate the Gamma textures. Then we prove the constant false alarm rate (CFAR) property of the proposed adaptive polarimetric detector. Finally, we take advantage of the simulated data and the real sea clutter data to evaluate the performance of the proposed polarimetric detector.