record phone calls on iphone

No. There is not. There is never likely to be such an animal. Aside from the technical limitations imposed by sandboxing applications and not allowing them access to core functions, Apple requires that apps be legal in all jurisdictions of the country in which they are sold. The laws in the US and most other countries vary from State to State, making this impossible for any call recording application.

You can believe what you like. The fact is, laws on recording phone conversations vary quite a bit from State to State in the US. Since there is only one US store, it would be virtually impossible for an app developer to come up with an app that would be legal in all jurisdictions.

In addition, the ability to do so would require access to core functions of the phone which Apple's APIs do not allow.

Fortune Hack wrote:

The fact is Windows and Google platforms permit recording of calls on their phones- thus your fact based on "law" is baseless;

No, it isn't. That Apple's requires all apps sold in the App Store be legal in all states has nothing to do with the Google's or Microsoft's terms of sale. They may not have such a policy. Apple has a number of policies regarding apps that are more restrictive than Google (does Microsoft even matter in this conversation?). Apple is free to sell or not sell the goods it choses.

Lawrence is also correct that such an app would require access to private APIs.

I'm not sure what you expect people to "brainstorm" about. The type of app you want doesn't exist and won't exist until a number of things change radically. No amount of discussion here is going to change that.