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Geometric distortions are generally simple and effective attacks for many watermarking methods. They can make detection and extraction of the embedded watermark difficult or even impossible by destroying the synchronization between the watermark reader and the embedded watermark. In this paper, we propose a new watermarking approach which allows watermark detection and extraction under affine transformation attacks. The novelty of our approach stands on a set of affine invariants we derived from Legendre moments. Watermark embedding and detection are directly performed on this set of invariants. We also show how these moments can be exploited for estimating the geometric distortion parameters in order to permit watermark extraction. Experimental results show that the proposed watermarking scheme is robust to a wide range of attacks: geometric distortion, filtering, compression, and additive noise.