The concrete-filled steel tubular (CFST) arch bridge has achieved significant development in recent years due to its unique mechanical performance and technical advantages. However, due to the lagging theoretical research compared to engineering practice, many problems have been exposed in the existing bridges, resulting in adverse social impacts and enormous economic losses. With the increasing prominence of safety issues in CFST arch bridges, it is necessary to assess their safety condition in service. This paper establishes a safety assessment index system for CFST arch bridges using the fuzzy analytic hierarchy process (AHP) based on an exponential scale. The assessment method proposed includes the following main points: (1) Bridge safety assessment is closely related to the load-bearing capacity of components. This study proposes an assessment index that comprehensively considers both the defect conditions and the design load-bearing capacity of components for the safety assessment. (2) The exponential scale method is introduced to safety assessment for the first time, and the AHP based on an exponential scale is applied to calculate the component weights. (3) Considering the specific structural characteristics of CFST arch bridges, this study provides a detailed division of component types and calculates the component weights. By combining the component assessment indexes, a comprehensive safety assessment index system is established, and a safety assessment method for CFST arch bridges is proposed. (4) Taking the Jiantiao Bridge in Zhejiang Province as an engineering case, the load-bearing capacity of components is calculated using finite element software ANSYS 19.1. Based on the established safety assessment index system, the safety of the bridge is assessed by integrating the inspection results. (5) Software for the safety assessment of a CFST arch bridge is developed using Visual Basic, and the assessment results align well with the actual condition of the bridge.