I have M-1 Visa. Can I apply for SSN?

Social Security numbers generally are assigned to people who are authorized to work in the United States. Social Security numbers are used to report your wages to the government and to determine eligibility for Social Security benefits. Social Security will not assign you a number just to enroll in a college or school.

If your school has authorized you to work either on or off campus, and you meet Social Security’s eligibility requirements described in the next section, you can get a Social Security number.

See here for details :

http://www.ssa.gov/pubs/10181.html