The earliest our international students can apply for a social security number is nearing the end of their program when applying for an OPT EAD card with the form I-765. You will receive your SSN in the mail within 1-2 weeks after receiving their OPT EAD card.
You may also apply for your SSN after receiving your EAD card in the mail. You'll need to take your passport, I-20, I-94, EAD card and form SS-5 to a social security administration office. You should also update your student account with your SSN.