SSN (Social Security Number) is needed to register for NCLEX-RN exam, also you must have SSN to be able to be allowed to work in any hospital in the US.
A Social Security number (SSN) is issued to track earnings over a worker's lifetime. Students holding F-1 student visa who are employed in the U.S. must apply for a Social Security number.
In order to issue a Social Security number, the Social Security Administration requires evidence that you are eligible to work in the U.S., that you are a full-time student, and that you have received a formal offer of employment through Curricular Practical Training, Optional Practical Training, or Academic Training. A Social Security number is not required to obtain a driver's license, cell phone, credit card, insurance, admission to an academic institution or other "non-work" reasons. The Social Security Administration must also verify your immigration documents and status with Immigration before issuing the Social Security number. Note that new students may not apply for a SSN earlier than 10 business days after arriving in the U.S. The Social Security number itself is not a work permit. Once approved you should be able to receive your SSN card usually within one week.