You could try downloading Soundflower, a freeware app that allows you to route audio between applications that don't normally "speak" to each other. I also own and use Wiretap Studio, but I like some of the effects available in Audacity's editor that are unavailable in Wiretap Studio, (i.e., cut, copy, paste, and reverse, among others), so I also use Audacity. Although I could simply import audio files recorded with Wiretap Studio into Audacity, I kept seeing references to Soundflower on the web and I was intrigued...I WANTED to be able to record streaming audio with Audacity if I chose to do so. I could already record vinyl lps in Audacity through my line-in port, and this would just add more functionality. I even saw Soundflower referenced on Audacity's Wiki page discussing issues pertinent to Mac users. See:
"No built-in streaming audio recording
Applies to: All Audacity versions
Macs almost always have no ability to record streaming audio internally off the built-in audio device. You could use Audio Hijack or Wiretap instead, which will capture the audio to AIFF files directly from the player application. Turn off compression in Wiretap Preferences if you want to import the recorded AIFF files into Audacity.
Alternatively if you are on OS X 10.2 and later you can use the free open source Soundflower system extension, on which Audio Hijack is based, too. Soundflower behaves like an additional system audio device, so for example to record streaming audio into Audacity you would select Soundflower as the output device in the application in which you are playing sound, and Soundflower as the input device on the Audio I/O tab of Audacity Preferences. If the application playing the sound does not allow you to specify its output device, you can make Soundflower the default output device in Apple Audio-MIDI Setup."
So, if you'd like, download Soundflower and install it. You won't see a window pane open up, but you should see a little flower icon in your menu bar. (If you want this to always be on, add it to your log-in items, otherwise, you'll have to open Soundflower every time you reboot.) You should probably make Soundflower your default system audio device. For easy switching, download a free app from Rogue Amoeba called Soundsource. It will appear as a little set of headphones in your menu bar. You can easily switch your input and output devices here. You should select "Soundflower 2ch" as your input device in the Soundsource menu.
Then, when you open Audacity's preferences, you'll have a choice to select your "recording" device as not just "built in line input" or "built in digital input" but also "Soundflower 2ch." (You can leave your output device as "built in line output.") When you want to record internet radio or other streaming audio, go to Soundsource and switch your system output device from "Line Out" to "Soundflower 2ch." Audacity should be able to "hear" and thus record any streaming audio coming through the system. When done, I like to go to Soundsource and switch system output back to "line out," simply because it allows me to adjust the system volume manually using the sliders and the keyboard; when the system output is selected as "Soundflower 2ch," you can't do this.
This may all seem complicated, as it did to me when I was reading about it, but it's really pretty easy once you try it. (Believe me, I am not techie, so if I can do this, you should be able to.)