Accurately assessing the structural integrity of cable-supported bridges hinges upon the precise determination of time-varying cable forces. In this study, a novel method is proposed for identifying these forces, even with the challenge of having only a single accelerometer available. Leveraging an improved Multisynchrosqueezing Transform (IMST) with an efficient ridge extraction algorithm, this method offers a robust solution. The IMST is employed to construct a clearer time-frequency spectrum based on the monitored acceleration response of a cable. Subsequently, the time-frequency ridge extraction algorithm enables the derivation of the cable's instantaneous frequency. Ultimately, the time-varying cable forces are computed by using the axially loaded beam theory and considering the influence of bending stiffness. Validations through a numerical benchmark model and a scaled cable testing confirm the efficacy of this approach. Result indicates that the average error in identifying cable forces is less than 2.50% in the numerical simulation. Moreover, the method is successfully applied to a real-world bridge scenario, demonstrating its ability to accurately evaluate cable forces despite having access to only a single-point noisy acceleration response.