Can my landlord take me to small claims if he is forcing me to pay a 3 month deposit, I’m an F1 student and had to break my lease?

Yes.

Your having no Social security Number is totally irrelevant as to what you might owe. As a matter of fact, what a person's SSN is should not even be mentioned in a trial. If you had a more than two month lease, then even if you gave 30 days notice before leaving, you would be liable for rent until the end of the lease period, but the landlord has to try to mitigate damages so must make reasonable efforts to try to re-rent the unit as soon as reasonably possible. Many judges consider 30 days to be enough time, especially when you give notice before leaving. If it was a month to month lease/rental, you are liable for only thirty days after you give written notice or when you move out, whichever is longer [so if your rent is due the first of the month and you give notice 11/15 that you will leave 12/15 and you pay the rent for that 1/2 month and leave by 12/15, you owe nothing in rent]. In California, I, the landlord can not require more than 2 months security deposit if the unit does not come with furniture and three months if it does. If the landlord sues you, he has to serve you with the suit; if you have left the country he can not serve you until you come back, and he will never know when you do.