I guess the sentence is in correct English grammar and style. But sounds strange to a Brazilian. Can someone tell why the sentence is “more correct” than the following?
She is a so persuasive girl.
It is a slightly uncommon construction, but your alternative is not grammatical at all. That’s because so here does not mean Portuguese muito but rather Portuguese tão. This is a common confusion between English speakers and speakers of Iberian languages, because the mapping isn’t what one might otherwise expect.
Think of this as a chopped-off so . . . as or perhaps as . . . as construction.
Imagine if the phrase had been:
She is not so persuasive a girl as her sister is.
She is just as persuasive a girl as her sister is.
(So it works more like tão . . . como . . . or tão . . . quanto . . . in Portuguese.)