<p>Corrugated steel web girder bridges offer significant advantages in terms of lightweight construction, cost-effectiveness, and enhanced durability, with their dynamic response being a critical factor influencing structural safety and performance under dynamic loading conditions. In this study, to investigate the impact of random road surface roughness on the dynamic response of corrugated steel web girder bridges, ANSYS finite element software and its APDL platform were used to establish a vehicle–bridge coupled model based on a corrugated steel web box girder bridge in China. A code is developed to implement a vehicle–bridge coupled vibration analysis method based on the contact constraint method. The analysis focuses on the dynamic response of the bridge under random excitation from road surface roughness, considering factors such as vehicle speed, vehicle configuration, and bridge surface roughness grade. The results show that the mean values of bridge displacement and bending moment responses are primarily controlled by the vehicle load on the bridge, with the maximum displacement and bending moment values occurring at a vehicle speed of 60 km/h. Moreover, increases in vehicle speed, vehicle load, and bridge surface roughness grade significantly amplify the dispersion of dynamic responses at the bridge mid-span.</p>