This manuscript presents the theory and design of a Vector-corrected Network Analyzer (VNA) realized in the acoustic domain. This is a novel measurement instrument based on the established microwave vector network analyzer. It employs directional couplers to separate forward and reverse traveling waves in acoustic waveguide. This instrument is intended to supersede the acoustic impedance tube. Advantages include greatly increased measurement speed and potential for traceability to external standards. Traceability is achieved by means of a calibration through an analytical solution of the error matrix produced from the measurement of a limited number of available acoustic standards. Operation is verified through analysis of the acoustic S-parameters of a passive, asymmetrical, reciprocal acoustic device constructed inside the acoustic waveguide. To the best of our knowledge this Acoustic Vector-corrected Network Analyzer (AVNA) is the first of its kind.