Post-earthquake functionality of bridges is critical to ensure emergency response and maintaining lifeline connectivity. This study investigates the residual traffic load-carrying capacity of a reinforced concrete (RC) deck-stiffened arch bridge after seismic ground shaking. This type of RC bridge was selected because it is frequently observed in the existing transportation infrastructure for its structural and aesthetic advantages. A comprehensive numerical framework was developed to assess the residual load-bearing capacity of the bridge after a design-level earthquake. A three-dimensional nonlinear finite element model was developed and validated against dynamic identification data. Spectrum-compatible ground motion records were selected and scaled according to Eurocode 8 and site-specific seismic hazard. Nonlinear time-history analysis was carried out to assess seismic performance and damage to the structural system. The presence of earthquake-damaged components was then considered into a subsequent robustness assessment of the bridge under traffic loads, based on incremental static (pushdown) analysis. Results reveal significant reductions in load-carrying capacity depending on the severity and location of seismic damage. The findings of this study offer insights into the seismic resilience of RC deck-stiffened arch bridges, informing post-earthquake inspection, traffic management, and retrofit prioritization strategies.