Yes - it is technically very doable, and there are lots of software packages to do it. But - just a word of caution. Be sure and check the laws in your state. There are some states where you must give a warning (which can be recorded) that the phone call may be monitored/recorded. This site will give you the particulars:
Eavesdrop
For example, in my state (Arizona, this is the law:
Ariz. Rev. Stat. Ann. § 13-3005: Interception of a wire or electronic communication by an individual who is not a party, without the consent of someone who is a party to the communication, is a felony. The electronic communications referred to in the statute include wireless and cellular calls. The overhearing of a conversation by an individual who is not present, without the consent of a party to that conversation, is also a felony. Both violations are classified as "class 5" felonies, which are the second least serious felonies in Arizona.
Under the statute, consent is not required for the taping of a non-electronic communication uttered by a person who does not have a reasonable expectation of privacy in that communication. See definition of "oral communication," Ariz. Rev. Stat. Ann. § 13-3001.
A state appellate court has held that a criminal defendant's contention that police officers violated this law by recording their interviews with him without his consent was meritless because the defendant had no reasonable expectation of privacy in a police interview room. Arizona v. Hauss, 688 P.2d 1051 (Ariz. Ct. App. 1984).
In addition, a state appellate court has held that a mother who had a good-faith belief that it was necessary and in the best interests of her child may consent to taping the child's conversation with an alleged child molester. State v. Morrison, 56 P.3d 63 (App. Div. 1 2002).
It is unlawful for a person to photograph or film a person without consent while the person is in a restroom, locker room, bathroom or bedroom or is undressed or involved in sexual activity. Ariz. Rev. Stat. Ann. § 13-3019.