Can you jailbreak iPhone 4S iOS 6.0.1?

I have 6.0.1 right now, theirs an update for 6.1.1. Should I update? Or is their a jailbreak for the 4s? If so; what website?

Take a look here http://thebesthostingweb.com

There's actually a way to jailbreak your iPhone 4S on iOS 6.1.2! It's called evasi0n. Just go to evasi0n.com to download it. I haven't actually used it, but it has good reviews and it has a "0" in place of an "o" like most legitimate jailbreaks do (LOL!).It also claims to be able to jailbreak any iPhone, iPod touch, iPad, or iPad mini on any version of iOS 6.

Hope this helps!

Yep you can. If you want to jailbreak the right way, here's a step by step tutorial on how to do it:

Here are some cool things you can download once you're jailbroken:

Hope this helps you out!