Boldbeast Call Recorder does just that
There are plenty of legitimate uses for a call recorder, but unfortunately the majority of use in the past has led device manufacturers to prevent easy call recording. If you’ve got a legitimate need to record calls, Call Recorder by Boldbeast Software can get most phones recording conversations without the need for root.
For the devices that aren’t supported, there are root-available options that will enable you to do what the device manufacturers have disabled. You’ll have to root your phone, of course.
Keep in mind in many jurisdictions, states, provinces, and countries recording conversations can be illegal without informing the person on the other line that is what you’re doing. In other places, such as Tennessee (where I’m at), as long as one person involved in the conversation knows it’s being recorded it’s legal.
There’s a free version and a pay version. The paid option allows you to automatically record calls whereas the free you have to push a button to start recording. You can store the recorded audio in WAV, MP4, 3GP, and AMR formats, most of which can be played by a computer with no special software required.
The free version floats a record button on the screen, and you can push it to start and stop recording, although on most devices it will stop when the system says there’s no longer a call in progress.
Recordings can be shared via most methods Android supports. Emailing them is a breeze, although the default AMR format you might have to download a codec or player for.
I can’t tell any difference in the quality between the original and the replay, however I’m not in an area that supports HD voice so it all sounds a bit cell-phony to me.
The pay auto-recording version is $9.99 but is phone-specific. You can change the phone it works on up to four times a year, so this shouldn’t be a problem for most of you.
The app also dynamically makes changes to the audio, but it doesn’t alter system settings. Uninstalling the app and rebooting your phone should solve any issues you might have with it.
Download: Google Play