She is so persuasive a girl

Solution 1:

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.

or even

She is just as persuasive a girl as her sister is.

(So it works more like tão . . . como . . . or tão . . . quanto . . . in Portuguese.)