"I'm sorry. Can I borrow your notes?"
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")
我可以向你借笔记吗 sounds weird, as a native speaker i wouldn't speak like that.
usually i'd just say 我可以借你的笔记吗？
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").
The grammar should otherwise be straightforward.