The species was first described scientifically by mycologists Melissa Danks, Teresa Lebel, and Karl Vernes in a 2010 issue of the journal Persoonia. The type collection was made in Mount Kaputar, New South Wales in July 2007. Molecular analysis of internal transcribed spacer sequences places Cortinarius basorapulus in the section Percomes of the genus Cortinarius, along with the European species C. langei, C. nanciencis and C. percomis. The specific epithet basorapulus is derived from the Latin words rapulum (a turnip) and baso (base) and refers to the distinct shape of the fruit bodies.