Zfe10's comment below seems to suggest that, yes, 借你的[noun] ("borrow your [noun]") is an acceptable (and perhaps even preferable?) alternative way to express 向你借[noun] ("borrow [noun] from you")
The "when", "where", and "how" information describing a verb must precede the verb in Chinese. "向你" is the "how" ("from you") and so must precede the verb "借" ("to borrow").