Cryo-electron microscopy (cryo-EM) single-particle image analysis is a powerful technique to resolve structures of biomacromolecules, while the challenge is that the cryo-EM image is of a low signal-to-noise ratio. For both two-dimensional image analysis and three-dimensional density map analysis, image alignment is an important step to improve the precision of the image distance calculation. In this paper, we introduce a new algorithm for performing two-dimensional pairwise alignment for cryo-EM particle images, which is based on the Fourier transform and power spectrum analysis. Compared to the existing heuristic iterative alignment methods, our method utilizes the signal distribution and signal feature on images' power spectrum to directly compute the alignment parameters. It does not require iterative computations and is robust against the cryo-EM image noise. Both theoretical analysis and experimental results suggest that our power-spectrum-feature-based alignment method is highly computational-efficient and is capable of offering effective alignment results. This new alignment algorithm is publicly available at: www.csbio.sjtu.edu.cn/bioinf/EMAF/for academic use.