Most stations (at least FM) have a website. They usually allow listening to their station via said website. As long as your net connection is good enough it should be pretty good, though not as good as over the air. All you'd need then is the software to GRAB the AUDIO.
If streaming isn't good enough quality, I'm sure there are USB or PCI(e) cards you can buy that will allow you to get the station over the air. This is usually bundled with cards that can record other things like VHS tapes, etc.
For example, my Pinnacle PCTV 340e Hybrid Pro USB tv-tuner stick, that I bought a couple years ago, handles not only tv but radio channels as well.
It was not exactly cheap, but it has some extra features like handling DVB-T, having a remote control, a little antenna, and some cables with which it can be connected to SVGA output, or VHS Player output. The dongle itself is not much bigger than a pendrive.
And it comes with dedicated software, which does recording too.
I bet you'll be able to listen to radio with most usb tv tuners.