Steel–concrete composite box beams are widely used in bridge engineering, which might bear transverse and longitudinal bending moments simultaneously under vehicle loads. To investigate the fatigue performance of joints between the steel girders and the top reinforced concrete (RC) slabs under transverse bending moments, a reduced scale joint between the weathering steel girder with the corrugated steel web (CSW) and the top RC slab was designed and tested under constant amplitude fatigue loads. Test results show that the joint initially cracked in the weld metal connecting the CSW with the bottom girder flange during the fatigue loading process. The initial crack propagated from the longitudinal fold to the adjacent inclined folds after the specimen was subjected to 7.63 × 105 loading cycles and caused the final fatigue failure. Compared with the calculated fatigue lives in the methods recommended by EC3 and AASHTO, the fatigue performance of the details involved in the joint satisfied the demands of fatigue design. Meanwhile, finite element (FE) models of joints with different parameters were established to determine their effect on the stress ranges at the hot spot regions of the joints. Numerical results show that improving the bending radius or the thickness of the CSW helps to reduce the stress ranges in the hot spot regions, which is beneficial to enhance the fatigue resistance of the investigated fatigue details accordingly.