Ultrasonic nondestructive testing is of great significance to ensure the working of equipment in aerospace, petrochemical, railway, and other fields. Transverse wave ultrasonic testing is an important method for the detection of internal defects in solids due to its advantages of weak attenuation of vibration mode, low sound speed, and high spatial resolution. However, due to the vibration characteristics of piezoelectric wafers, conventional ultrasonic transducers cannot directly transmit and receive transverse waves and need to refract the transverse waves with the help of oblique incidence, and due to the particularity of oblique incidence, it is necessary to consider the refraction effect and slope detection simultaneously, which increases the burden of ultrasonic imaging reconstruction calculation. Therefore, a wavenumber-domain fast reconstruction technique using ultrasonic scanning for transverse waves is proposed. The method is built based on classical synthetic aperture focusing technology (SAFT) by integrating the coordinate transformation in wavenumber domain and transverse wave wavefield extrapolation for the application of oblique incidence transverse wave imaging. The simulation and experimental results show that the proposed method can build excellent detection results when detecting transverse holes, cracks, and hemispherical flat-bottom holes with refraction angles from 20° to 60°. Compared with the time-domain synthetic aperture focusing technique, the computational efficiency of this method is improved by at least 100 times without losing the reconstruction accuracy.