from service canada website:
What information/documents do I need to apply?
Temporary residents
You must provide one of the following primary documents:
Work permit issued by Citizenship and Immigration Canada (CIC).
Study permit issued by CIC. International students must present either:
a study permit that indicates the permit holder “may accept employment” or “may work” in Canada; or
a study permit and a “confirmation to work off campus” letter issued by CIC prior to February 6, 2015.
If neither of these requirements is met, you may contact CIC to verify if you are eligible to apply for an amended study permit.
Visitor record issued by CIC, indicating you are authorized to work in Canada.
Diplomatic identity card and a note of permission of employment issued by Foreign Affairs, Trade and Development Canada.
So considering you are not authorized to work or study in canada and you are a visitor, no you are not eligible to apply for a SIN#. A SIN# is specific to work and government services, and visitors certainly aren't eligible for either.