As the Grammarly blog has it: "The vice in vice versa is not the same vice that means moral fault, but it is the vice we use in phrases like vice–president. It comes from the Latin word vicis, which means 'a change,' 'an alteration,' or 'a succession,' but also 'a place' or 'a position.' Versa comes from versus, which means 'to turn.' When you combine the two words, you get a phrase that literally means 'with position turned,' or, as we like to say in English, 'the other way around.'"
According to Oxford Reference, vice versa literally means 'in–turned position'.
My Latin is more than a little rusty, but I prefer Grammarly's version. (Even if it is American. In British English, I think we would prefer to say "the other way round".)
© Haydn Thompson 2020