Wirelessly posted (Mozilla/5.0 (iPhone; CPU iPhone OS 5_0_1 like Mac OS X) AppleWebKit/534.46 (KHTML, like Gecko) Version/5.1 Mobile/9A405 Safari/7534.48.3)
Icom says you can do it... If you purchase their adapter (described below from Icom's R20 specs)-
Built-in 260 minute Digital (audio) recorder
The IC-R20 has a built-in 32MB Digital (audio) recorder*1, which allows you to record received audio for up to 260 minutes. The IC recorder is useful in a variety of ways, like recording wireless microphone audio at a meeting. Recording qualities are selectable from HQ, SP and LP modes and playing speed is adjustable from ×0.5 to ×1.5. Used with the optional CS-R20, you can transfer the recorded contents to your PC and store them*2.
*1 Records received radio audio only
Cannot record external speech etc
*2 Cannot play recorded contents on your computer