The ぜ at the end makes it sound rather rough and very colloquial. You wouldn't want to say this to a stranger, as it would be very off putting, but perhaps you may already know this. In fact, you likely will never use ぜ at all, even with close friends. The impression I get is that it's mostly used by kids and has a kind of "cool factor," but it's not really used in standard Japanese conversation. You'll hear it a lot in anime, but what is said in anime usually differs greatly with the norm.
In any case, a more natural phrasing of this expression might be:
「これからよろしくお願いします!」or「これからよろしくお願い致します!」
Both of these forms are very polite and is kinda difficult to translate into English, given that we don't really have anything like this. It's a very cultural phrase and the translation will depend on the context. However, in a general sense, you might translate it as: "I look forward to working with you in the future." This kind of phrase is often used when you have just met with a new co-worker, or if you have requested someone's assistance. It's a formal business type of phrase, usually, but can apply to minor everyday situations as well.
I hope this helps you. If you have any more questions, let me know.