Assuming that you are an F-1 student, you do have a work authorization. The previous post by Cookie covered that issue.
If you desire to work more than 20 hours a week and have less hassle trying to find an internship or a job, you might try to get a work-authorization social security number.
You may obtain a social security number (SSN) by providing proper documentation and completing a form SS-5 (an application for Social Security Card).
When applying for SSN (if you have F-1 visa) you will need to present your passport with the visa, I-94 Card, I-20-ID form with a work authorization letter from your university.
If you have a J-1 visa, you might be automatically authorized for work, if you’re not…you will require the permission of your sponsor(s). When applying for an SSN, the J-1’s must present their passport with the visa, I-94 Card, IAP-66 and a completed SS-5 Form.
This site will give you more information on how to obtain your SSN
it might seem a bit overwhelming but in the long run, having a SSN will make your life much easier.