Can I JailBreak iPhone 4 on iOS 7?

Hi. I've recently bought used iPhone 4 iOS 7.1.2, not jailbroken, but logged into iCloud (I can used it but it's logged by previous user). I wonder if I can JailBreak it now without updating it to iOS 8 (or iOS 6)? Is it possible, because some people told me it isn't on iOS 7.

Yes!

You have to use Pangu jailbreak to jailbreak iOS 7.1.x

You can download it from here: http://en.7.pangu.io/