International students without a Social Security number (SSN) are unfortunately ineligible for an Illinois State ID card. However, you may apply for a temporary visitor driver's license by showing an SSN letter of ineligibility (or denial letter) issued by the Social Security Administration, along with your passport, and copies of your apartment rental/lease agreement or an official document from SAIC such as a piece of mail or Enrollment Verification form. For more information check the Secretary of State’s website.
You may drive in Illinois with your valid license from your home country while attending SAIC. You should have a copy of your driver’s license from your home country with you when you drive. If you are pulled over, the police officer may also request a translation in English from you. Illinois does not recognize the International Driving Permit (IDP) as a valid license. If you plan to drive, you may want to read Illinois's Rules of the Road.