Although the role of WRKY transcription factors (TFs) in colour formation has been reported in several species, their function in potato (Solanum tuberosum L.) anthocyanin biosynthesis remains unclear. In this study, the potato WRKY gene StWRKY13 was isolated and characterised. Expression analysis revealed a significantly higher StWRKY13 expression in chromatic tubers than in yellow ones. Transient activation assays showed that StWRKY13 could enhance the role of StAN2 in promoting anthocyanin biosynthesis in tobacco (Nicotiana tabacum L.). Over-expressing the StWRKY13 gene promoted anthocyanin biosynthesis in potato tubers. Further investigations indicated that StWRKY13 could interact with the StCHS, StF3H, StDFR, and StANS gene promoters and significantly enhance their activities. Our findings showed that StWRKY13 could promote anthocyanin biosynthesis by activating StCHS, StF3H, StDFR, and StANS transcription in potato tubers, thereby supporting the theoretical basis for anthocyanins formation in coloured potato tubers.