As other people have said, it was borrowed from the Italian fascists, who themselves got it from an 18th century painting showing a famous event from Roman history/legend. There’s no evidence that it was ever actually used in Ancient or Classical Rome.

Funny side story is that some Nazis and other German nationalists thought it wasn’t ‘German’ enough, so the leading Nazis felt they had to invent an older ‘Germanic’ tradition to justify its usage. So, it’s a fake German tradition that was in fact borrowed from the Italians, who got it from a fake Roman tradition that was actually made up by a French guy.