It's worth noting that the Romans never did this. There was a fairly brief period in the 19th century where it was kind of a pop-culture Roman thing (it showed up in plays about Ancient Rome, that sort of thing), and then it was adopted by various nationalist groups, including the Italian fascists, and, ultimately, the Nazis.
Unless you're a theatre fan who's been in a coma for the last 150 years, though, it's a fascist (or Nazi) salute; the use of the 'roman salute' term is (potentially accidental; I think maybe some people do think it was a real thing) sanewashing.