Waterborne debris during storm surge events can impose significant impact loads and thereby cause severe damage to coastal structures. While several studies have characterized debris impact loads, very few studies have actually focused on the structural behavior and vulnerability of coastal structures, like bridges, subjected to such impacts. This study investigates the structural response of a case study bridge subjected to water-driven debris impacts and develops its associated fragility model during storm surge events. First, the hydrodynamic conditions at the bridge location are defined. Next, finite element models of the debris and a typical pier system of the case study bridge are developed and validated to compute the demands imposed on a column by the impact of the debris. An analysis of variance (ANOVA) is then conducted to study the influence of different parameters on the imposed demands. Finally, a statistical sampling method and logistic regression are used to derive a fragility model and assess the vulnerability of the case study bridge. The resulting fragility models can be used for rapid vulnerability assessment, evaluation of mitigation strategies, and to obtain key insights concerning the effects of each parameter on the probability of shear failure of a bridge column under debris impact.