The turnout switch rail is a type of variable-cross-section rail, and its irregular structural characteristics result in complex ultrasonic guided wave detection signals. When employing the reflection method to detect cracks in the rail base, the amplitude of the echo signal cannot represent the size of the crack. To quantitatively analyze the crack signals, a method that combines deep learning and ultrasonic guided wave technology is employed to quantitatively assess the depth of cracks in the rail base of the turnout switch rail. By applying wavelet transform to obtain wavelet time–frequency diagrams, four deep learning models—GoogLeNet, Mobilenetv1, Mobilenetv2, and Mobilenetv3—are utilized to classify the depth of cracks in the rail base, and the performance of these models is assessed using experimental data. The experimental results show that the combination of the Mobilenetv3 deep learning model and ultrasonic guided wave technology achieves a 95% recognition accuracy for the quantitative detection of cracks in the rail base of turnout switch rails. This research work provides a foundation for the feasibility and reliability of combining deep learning models with ultrasonic guided wave technology for the quantitative detection of crack depths in turnout switch rails.