Asking the primary professor of your target grad school to review your statement of purpose I'm applying for a PhD in the US (I'm from Italy).

I was thinking that maybe I could ask the primary professor of the school I'm applying for to review and give me his opinion about the statement of purpose I'm writing.

I'm afraid though, that in the US academic environment, this could be seen like ethically not fine. In Italy this would not be a problem, but I want to avoid to hit a cultural difference.

Is it something appropriate?
Your hunch is correct.  It would not be ethical.

However, if you have a mentor in your current institution, you can certainly send this person a link to the primary professor's home page, and your essay, asking for feedback.

But before you do, here's a pretty effective exercise.  Imagine that the trusted mentor is reading your essay and jotting down comments in the margin, slashing here, asking for more detail there.