Yes, but you would have to be jailbroken.
It's called "CallerIdFaker" it gives you the option to record your whole conversation with other people. But Remember that recording other people on the phone without their permission is illegal.. The law says you have to let them know they are being recorded..
Like if you call 1800-MyApple it would always say "this call MAY BE RECORDED for quality and training purposes"
Hope this helped! =)