Can I record a phone call on an iPhone? Nothing more to say than "Is there an app to record the current phone call ?" :-)
Beware of legal issues.

You can but you'll need to jailbreak, use extra hardware (plug a mic into the headphone jack), or use 3rd party SIP software. For example, Google Voice has an iPhone app, and Google Voice supports call recording. Google Voice does announce to both parties that it is recording the call.