If you are issued a new Social Security number (SSN), you should bring your SSN card to the Registrar to have your student record updated and then visit the ID center for a new one with the correct SSN encoded. You will need a new card because your identity in the ID card system is based on your SSN.

Morningside Campus

Office of the Registrar 
Columbia University 
210 Kent Hall, MC 9202 

Medical Center Campus

Student Administrative Services 
Columbia University 
650 W. 168th Street 
Unit 45, Black Building 1st fl., Room 141