What is necessary will be "a lot", if I understand your question correctly. First, you would need to build your own shield (I don't think there exists a "cell phone" shield, but who knows?); I do know that SparkFun sells cellular modules that can use your sim card:http://www.sparkfun.com/commerce/categories.php?c=66
Note that many of them aren't cheap; but, several (seem?) to not require anything more than a USB connection, but that may be data only, and not audio. In fact, I am not sure which would allow for you to use the PC (or the PC via an Arduino) to send the AT dialing commands and such (I presume this is what you want to do), then allow the voice/headset to be used to talk over the cellular module like a cell phone. You'll have to review them.
Beyond that, you would then need software on the PC side that could allow the selection (in some manner) of the phone number to dial, then send that via USB to the Arduino (or directly to the module), which would then interpret it and send/use the appropriate AT commands (or whatver protocol) to cause the module to dial and conncect; it would also have to monitor the status, so it knows if the call is connected, failed to connect, and/or what the signal strength is before, during, and after the call.
Sounds like an ambitious project, but certainly doable if you don't mind spending more money than it would cost to buy a cheapo TracFone...