Is it normal that iPhone 4S touch screen is not working correctly when charging
That's definitely not normal behaviour!

It could be something to do with earthing or voltage though as the screen is capacitive, so try charging from another source to see if it does the same thing. e.g. if you're charging from USB on your computer, try it on another computer if possible, or with the mains adapter. If that fixes your problem, it's possible you have a voltage issue or earth leakage issue on the port.

If it doesn't fix it, then the problem is likely with the iPhone itself.

I've had problems in the past where I was charging my iPhone on a work PC and sometimes when I touched the phone it would reset it. Luckily there was no damage caused, but it was a little weird.