The accurate measurement of cable force plays an important role in the structural form, structural behavior, and safety evaluation of large-span cable-stayed bridges. A fast cable-force estimation method is proposed based on the alignment recognition method and smartphone-captured video. This method can realize real-time, non-contact, and non-destructive force measurements. Videos of bridge cables were collected using a portable smartphone, and an alignment recognition method was employed to obtain the lateral displacement along the cable, followed by numerical differentiation of the lateral displacement of the cable to acquire the acceleration time history. Based on the fundamental dynamic equation of beam elements, a unified explicit formula for cable-force calculation considering service characteristics was established in the frequency method. Finally, the method was applied to the cable-force measurement during the operation and maintenance stage of the Gengcun Dou Bridge. The measured cable forces were compared with the values obtained from the on-site monitoring system. The results show that the proposed method can accurately identify the acceleration time history at different positions of the cable, and the corresponding frequency components are essentially consistent. The average relative deviation of the measured cable forces from the reference method is within 3%. The proposed cable-force measurement method is simple as regards equipment, convenient for operation, and high in efficiency, providing a new method for the measurement of cable forces in large-span cable-stayed bridges, which can offer reliable measured cable-force data for structural analysis during bridge operation and the maintenance stage.