A robust feature points detector for invariant audio watermarking is proposed in this paper. The audio segments centering at the detected feature points are extracted for both watermark embedding and extraction. These feature points are invariant to various attacks and will not be changed much for maintaining high auditory quality. Besides, high robustness and inaudibility can be achieved by embedding the watermark into the approximation coefficients of Stationary Wavelet Transform (SWT) domain,which is shift invariant. The spread spectrum communication technique is adopted to embed the watermark. Experimental results show that the proposed Robust Audio Segments Extractor (RASE) and the watermarking scheme are not only robust against common audio signal processing, such as low-pass filtering, MP3 compression, echo addition, volume change, and normalization; and distortions introduced in Stir-mark benchmark for Audio; but also robust against synchronization geometric distortions simultaneously, such as resample time-scale modification (TSM) with scaling factors up to %, pitch invariant TSM by %, and tempo invariant pitch shifting by %. In general, the proposed scheme can well resist various attacks by the joint RASE and SWT approach, which performs much better comparing with the existing state-of-the art methods.