I have seen many sites claiming they have a jailbreak for iOS 9.3.1, but no one is available, just to cheat traffic. The below are some of the jailbreak status I know:
Due to Apple responded quickly to kill the Pangu Jailbreak by releasing iOS 9.1, which patched several vulnerabilities used by the jailbreak tool. It continued patching some more exploits in iOS 9.2 and iOS 9.2.1 used in the Pangu Jailbreak. But Pangu team responded recently, by releasing a new version of their Pangu Jailbreak tool to jailbreak iOS 9.1. Unfortunately, it doesn’t work with iOS 9.2, iOS 9.2.1, iOS 9.3 or iOS 9.3.1.
So at present we can only jailbreak iOS 9.1 and lower, higher version is not available