I rent my basement. I bought new furnace. Can I claim furnace cost against rental income?

You will be able to claim the portion of the furnace cost that relates to the size of the rental space in comparison to the rest of the house.  Square footage of the rental suite divided by the total square footage of the house will give you the percentage.

http://www.cra-arc.gc.ca/tx/bsnss/tpcs/rntl/bt/rprt/ln9949-eng.html

so do I consider it a capital asset that depreciates and enter it that way?

Replacement of a furnace would not usually be capitalized unless the house did not have one to begin with.  If that was the case, the value of the furnace would be added to the value of the house, not done separately.  It should probably be an expense.