The RNA-dependent RNA polymerase (RdRP) is the only homologous gene shared among current members of the kingdom Orthornavirae in the realm Riboviria. It is therefore used as a hallmark gene to infer their evolutionary relationships, and to guide their taxonomic classification. While sequence similarity between RNA viruses is often limited and sequences problematic to align, the conservation between the three-dimensional tertiary structures of viral RdRPs is notable, supporting analysis of deep evolutionary relationships. Nevertheless, the limited availability of experimental RdRP structures restricts structure-based phylogenetic analyses. We used protein structure prediction algorithm AlphaFold to alleviate this restriction and predicted structure models for 989 viral RdRPs. Through structural alignment with Homologous Structure Finder, we identified 211 structurally equivalent residues for RdRPs, representing 96 virus genera recognized by the International Committee on Taxonomy of Viruses. These equivalent residues were used to deduce a comprehensive structure-based phylogenetic tree for viral RdRPs, which was validated using a jackknifing approach developed in this study. For comparison, structural phylogenies were inferred using alignments produced with FoldTree and FoldMason software. The resulting trees mostly support the current taxonomic assignments of RNA viruses at the class rank. However, they do not support the monophyly of phyla Pisuviricota and Duplornaviricota. Furthermore, flaviviruses frequently group apart from other members of Kitrinoviricota. The conservation of protein structures over long periods of evolutionary time, when detectable sequence homology may be lost and sequence alignment problematic, supports the use of protein structure comparison methods for demonstrating the deeper evolutionary histories of RNA viruses.