Synthetic aperture radar (SAR) is considered being a good option for earth observation with its unique advantages. In this paper, we proposed an adaptive ship detector using full-polarization SAR images. First, by thoroughly investigating the scattering characteristics between ships and their background, and the wave polarization anisotropy, a novel ship detector is proposed by jointing the two characteristics, named Scattering-Anisotropy joint (joint-SA). Based on the theoretical analysis, we showed that the joint-SA is an effective physical quantity to show the difference between the ship and its background, and thus joint-SA can be used for ship detection of full-polarization image data. Second, the generalized Gamma distribution was used to characterize the joint-SA statistics of sea clutter with a large range of homogeneity. As a result, an adaptive constant false alarm rate (CFAR) method was implemented based on the joint-SA. Finally, RADARSAT-2 and GF-3 data in C-band and ALOS data in L-band are used for verification. We tested on five datasets, and the experimental results verify the correctness and superiority of the constant false alarm rate (CFAR) method based on the joint-SA. In addition, the experimental results also showed that the signal-clutter ratio (SCR) of the proposed ship detector joint-SA (33.17 dB, 35.98 dB, 57.25 dB) is better than that of DBSP (8.92 dB, 3.43 dB, 25.40 dB) and RsDVH (17.28 dB, 11.17 dB, 54.55 dB). More importantly, the proposed detector joint-SA has higher detection accuracy and a lower false alarm rate.