Have you restarted your iPhone, hold down both Home button and Power button until the apple logo appears. Wait for phone to restart. It's like rebooting your computer.
If that doesn't help try resetting network settings, Settings => General => scroll down to Reset => Reset Network Settings
You will have to reenter your password.
Also have you updated iOS to 6.0.2? It was created for iPhone 5 and Mini iPad wifi problems.