Rotation and scale estimation of images are fundamental tasks in image registration. The conventional estimation method uses log-polar transform and 1D shift estimation to estimate rotation and scale regardless of the shift of images. However, this transform requires interpolation of the frequency components, which causes estimation error. We propose a rotation and scale estimation algorithm based on Radon transform and sub-pixel shift estimation. Radon transform can estimate the rotation independent of the shift and can reduce the influence of interpolation error because it is performed on the spatial image rather than the frequency. In addition, sub-pixel shift estimation using linear approximation of the phase component improves the precision of 1D shift estimation and achieves accurate rotation estimation. The proposed method was evaluated on test images, and the results demonstrate that the proposed method accurately estimates rotation compared to log-polar-based and other conventional methods.