International Students Working
International Students are allowed to work in the United States, however, the U.S.A. has very strict rules. Students with F-1 or J-1 visa can only work with authorization from a Designated School Official (DSO) or Alternate Responsible Officer. A social security card is not authorization.
Below is information about the types of work authorization that are permitted.

F-1 and J-1 students are eligible for on-campus employment immediately upon arrival. Learn more here.

F-1 students become eligible for Curricular Practical Training (CPT) after one academic year of study. Curricular practical training (CPT) is an alternative work/study, internship, cooperative education or other type of required practicum that a sponsoring employer offers through cooperative agreements with your college or university. CPT is only available for F-1 students when it is part of an established curriculum within a school. CPT must be integral to your program of study. Learn more here.

Optional Practical Training (OPT) is a form of training, often paid, that directly relates to your program of study. You can apply for OPT during your program of study, which is known as pre-completion OPT, or after you finish your program of study, know as post-completion OPT. Learn more here.
Government Links
Study in the States - Working in the United States
Social Security Administration - International Students and Social Security Numbers
U.S. Immigrations and Customs Enforcement (ICE) - Employment