Published on Brock University (http://www.brocku.ca)
Check related information on CIC website for new procedure on applying SIN for working off-campus:
If you are holding a Study Permit issued after June 1, 2014 (with a remark says that you may work off-campus), you could go to Service Canada office to apply SIN directly. See Service Canada St Catharines office's address below.
If you are holding a Study Permit issued before June 1, 2014 or without the remark indicating that you may work off-campus, you must submit a request for an amendment to your study permit before you can apply for a SIN. There is no fee for this request. http://www.cic.gc.ca/english/information/applications/amend.asp 
Check CIC website for more information: http://www.cic.gc.ca/english/study/work-offcampus.asp 
Then go to Service Canada office to request SIN.
You will receive the SIN the same time you visit Service Canada office.
Service Canada office in St. Catharines:
395 Ontario Street
St. Catharines, ON, L2N 7N6
Telephone: 1 800 206 7218 option 3
Hours: Monday to Friday 8:30 am – 4:00 pm
More information on Service Canada website: