Registration of optical and synthetic aperture radar (SAR) images is challenging because extracting located identically and unique features on both images are tricky. This paper proposes a novel optical and SAR image registration method based on relative total variation (RTV) and scale-invariant feature transform (SIFT), named RTV-SIFT, to extract feature points on the edges of structures and construct structural edge descriptors to improve the registration accuracy. First, a novel RTV-Harris feature point detection method by combining the RTV and the multiscale Harris algorithm is proposed to extract feature points on both images’ significant structures. This ensures a high repetition rate of the feature points. Second, the feature point descriptors are constructed on enhanced phase congruency edge (EPCE), which combines the Sobel operator and maximum moment of phase congruency (PC) to extract edges from structured images that enhance robustness to nonlinear intensity differences and speckle noise. Finally, after coarse registration, the position and orientation Euclidean distance (POED) between feature points is utilized to achieve fine feature point matching to improve the registration accuracy. The experimental results demonstrate the superiority of the proposed RTV-SIFT method in different scenes and image capture conditions, indicating its robustness and effectiveness in optical and SAR image registration.