Self-assembly of gold nanorods (NRs) in linear, polymer-like chains offers the ability to test and validate theoretical models of molecular polymerization. Practically, NR chains show multiple promising applications in sensing of chemical and biological species. Both areas of research can strongly benefit from the development of a quantitative tool for characterization of the structure of NR chains in the course of self-assembly, based on the change in ensemble-averaged optical properties of plasmonic polymers; however, quantitative correlation between the extinction spectra and the structural characteristics of NR chains has not been reported. Here, we report such a tool by a quantitatively correlating the red shift of the longitudinal surface plasmon band of gold NRs and the average aggregation number of NR chains. The generality of the method is demonstrated for NRs with different aspect ratios, for varying inter-rod distances in the chains, and for varying initial concentrations of NRs in solution. We modeled the extinction spectra of the NR chains by combining the theory of step-growth polymerization with finite-difference time-domain simulations and a resistor-inductor-capacitor model, and obtained agreement between the theoretical and experimental results. In addition to capturing quantitatively the ensemble physics of the polymerization, the proposed 'plasmonic counter' approach provides a real-time cost- and labor-efficient method for the characterization of self-assembly of plasmonic polymers.