Point matching has attracted important attention in radar signal processing while the targets can be modeled by point sets to realize their recognition. Due to the different imaging parameters or viewpoints, the images captured by different synthetic aperture radar (SAR) sensors suffer from distortions. Since the distortions between images can be approximated by affine transformations, the key problem for point matching is to extract affine invariant descriptors. Moment, which has been widely used for point matching, limits to affine transformations as their support point set (SPS) can’t keep invariant. To address this problem, AICT is proposed as a rigorous affine invariant SPS. It is constructed by a recursive process: the point set is first divided by the vector from the certain point to the centroid of the point set, and the centroids of subsets are used to generate vectors which induce new partitioning. In addition, the centroids of the subsets are stored in order to form the AICT of the point. AICT, which represents the inherent structure of the point set, highly tolerant to noise and outliers due to the global nature of our partitioning process. More importantly, it is affine invariant owing to the affine invariance of centroids and relative position. Therefore, we can get a new rigorous affine invariant descriptor while moments are computed based on the points in AICT. The experimental results on synthesized and real data validate verify that our proposed algorithm outperforms the state-of-the-art point matching methods including SC, ICP, and TPS-RPM.