Not that I know of. There used to be an app that did this by using a workaround involving AirPlay, but predictably, Apple removed the app within a day.
Short answer: No - it's against Apple's App Store rules.
Long Answer: Even if you were to tether to the Mac (or PC), it would be difficult (or expensive) to get the sound as well. If you're willing to pay, Adobe Captivate will capture the screen, audio, and gestures (though it's a tethered solution).
What are you trying to capture? If it's an app demo (and you REALLY can't tether to a computer), you could always take Screen Caps, bring into iMovie and record narration.
Found this app, may want to grab it and give it a whirl, because there's no telling how long it will remain online. Haven't personally tried it though.