George Lucas estava que fez esta pergunta durante as filmagens de 'Revenge of the Sith'. Basta dizer que sua resposta não foi nem esclarecedora nem especialmente significativa.
"So how did Anakin get that scar, George?" asks John Knoll.
"I don't know. Ask Howard," says George, referring to President of Lucas Licensing Howard Roffman. "That's one of those things that happens in the novels between the movies. I just put it there. He has to explain how it got there. I think Anakin got it slipping in the bathtub, but of course, he's not going to tell anybody that."
O livro a que ele está se referindo é "A Ascensão e Queda de Darth Vader", que nos informa que sua cicatriz foi recebida durante um duelo com Asajj Ventress.
Lethal droids were not the only adversaries to the Jedi, as Count
Dooku had recruited such deadly beings as the Sith aspirant Asajj
Ventress and the nearly indestructible Gen'Dai bounty hunter, Durge,
to fight on his behalf. Dooku himself had trained Ventress in the art
of lightsaber combat, but often ridiculed her preference to wield two
lightsabers at the same time. Anakin nearly defeated Ventress on the
fourth moon of the gas giant Yavin. One of their duels, in the
industrial sector of Coruscant, left him with a deep scar on the right
side of his face.
The Rise and Fall of Darth Vader
Na verdade, vemos esse evento na série de quadrinhos Republic 71: Dreadnaughts of Rendili, Parte 3