The only method I know of is Google Voice. There used to be a few from the AppStore but they breached the privacy laws so they were removed. But there is an old method that I'm not entire sure that it still works, so give it a try maybe with your home phone or through Google Voice.
1. Be in a call with person
2. Hit the (+) button on your keypad to add a number
3. Type in your phone number
4. It will go strait to voicemail
5. Once you here the beep, it will start recording
6. When you hang up the call, you will get a voicemail of your recording