GuitarPort from Line6 ís more or less exactly this piece of hardware you need to convert the signal to something digital . The software that comes with it does the rest, no need for a real extra soundcard actually, even an old PC will do fine...

With GuitarPort you can also choose to subscribe to an online network (7$/mnth) and do collaborations with people all across the world, get lessons from people in other countries and so on, but even without access to the online network you can just playback MP3s and so on to jam along with, together with having the ability to do a lot of other things (like record your music).

It's pretty cool.