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.