There are two types of cell phone service in the US: prepaid service and contract service. SSN (Social Security Number) is require for contract service, so if you do not have one, you will have to use prepaid service.
Although a contract with a major carrier may be a good choice for someone who will be here long term, it would not be a good choice for anyone who will be here for less time than the contract requires.
Another option for making international calls is to download a video and voice chat client, such as Skype. This can be a cheaper alternative than a cell phone; however, it is not as convenient.