CyanogenMod team are adding a much awaited feature. Users of selected devices can now get FM radio on CM10.1, CM10 and CM9 ROMs. The feature is currently limited to some specific devices though and is said to be working on devices with Qcom / Broadcom Wi-Fi chips that have support for FM radio. This has been confirmed for Sony devices with these chips however it may or may not be compatible with your device. As per CyanogenMod team:
This has been tested on a handful of devices, however final support for your device will be up to compatibility of the chips, kernel and for the maintainer to enable. Currently, 8960 devices are showing some issues.
So, a lot of Sony Xperia devices with FM radio functionality are supported. What’s commendable, apart from the hard work of CyanogenMod team, is Sony’s support. It won’t be possible without support from Sony. As mentioned by CM team themselves:
Much of this comes from working with the folks at Sony and they are looking to push this support upstream to AOSP as well.
Once the support is added, all you will have to do is to use your headset as antenna and fire up the FM radio. For more information and to see the official post by CyanogenMod, head over to this post on their Google Plus page.