How to update my 3GS to 6.1?

I have an iPhone 3GS and it only charges when it's turned off because the charger hold inside, some of it's broken off. But I can get any apps and the software on it is 4.1 and I'd like to update to 6.1 but I can't plug the device into iTunes because it only charges when it's turned off and I tried it before, it doesn't consecutive to iTunes when I do plug it in.mis there another way to update my phone?

You can't. IPhone 3GS can't upgrade to iOS 6