Climate change impacts the infrastructure in several ways. In the particular case of bridges crossing rivers, climate change may have a direct impact on the river discharge and, consequently, may modify the bridge scouring patterns. The significance of the scouring phenomenon is related to its effect on the reliability of the bridge since the structure's capacity rapidly decreases due to local scour causing sudden failure. Therefore, estimating the impact of climate change on the scouring risk is important within the context of bridge reliability analysis. This problem is addressed in this paper by introducing a Lévy process shock degradation model to present the changes within the scour depth of a typical bridge considering several Representative Concentration Pathways scenarios (RCPs). The scour depth is calculated using the HEC-18 Design model and the threshold of failure is considered the foundation depth. This paper presents the impact of climate change on the structure's safety, the results present the independent rapid decrease in the structure's capacity, the long-term availability, the expected lifetime of the bridge before failure, the probability of failure, and the Priority Rating Ratio of the bridge due to local scour.