Due to their unique advantages, surface acoustic wave (SAW) sensors have attracted various disciplines to carry out thorough research. However, in their wireless applications, their high carrier frequency, low signal-to-noise ratio, and short effective signal length have led to poor signal measurement accuracy and complex detection systems. Using an SAW torque sensor as its objective, this paper describes the proposal and completion of a novel processing system based on compressive sensing (CS). The system was implemented using an analog-to-information conversion module. The module hardware’s structural parameters and signal recovery parameters were designed and optimized by simulation. Furthermore, an intervening interpolation method based on support vector machine (SVM) signal secondary information prediction was developed to achieve an effective extension of the observed signal. The method’s parameters and the SVM super parameters were optimized by a cuckoo search algorithm. The success rate of the predicted signal secondary information reached more than 94%. The compression ratio of the system reached 5.77‰ while ensuring successful signal frequency recovery. Finally, a torque static calibration experiment was carried out using the system prototype; the results show that the system sensitivity is 1.951 kHz Nm−1, which proves that the scheme and methods are effective. The SAW signal-processing system based on CS combines the advantages of traditional demodulation system solutions with low hardware costs, low data volume, and high interference immunity. This system will prompt some new thoughts about SAW sensor signal detection.