ward's got it right. Just as an amplifier has circuitry to "do something" with your analogue signal, there has to be circuitry to "do something" in your computer. This "something" is analog-to-digital conversion, which is something that any soundcard can do. But a USB port is not a soundcard, and it doesn't 'tap into' your soundcard's converters either.
If you want something like what you're describing, but not as a DIY solution, there are a few products on the market. The one that springs to mind is the IK Multimedia Stealthplug, which includes Mackie Tracktion 2 recording software (worth the price of admission by itself!) and a lite version of Amplitube, an amp-modeling software. The Stealthplug isn't the best 'soundcard' on the market, but it does an adequate job and the price can't be beat for that package.