We demonstrated an automated passive-transmission-line routing tool for single-flux-quantum (SFQ) circuits. The tool is based on the A* algorithm, which is widely used in CMOS LSI design, and tuned for microstrip/strip lines formed in the SRL 4-Nb layer structure. In large-scale SFQ circuits with 10000-20000 Josephson junctions, such as microprocessors, 80-90% of the wires can be automatically routed in about ten minutes. We verified correct operation above 40 GHz for an automatically routed 44 switch circuit from on-chip high-speed tests. The resulting circuit size and operating frequency were comparable to those of a manually designed result. We believe that the tool is useful for large-scale SFQ circuit design using conventional fabrication processes.