No, landlord IS the home warranty

Legally, landlord offers a warranty of habitability when he/she put the unit for rent. This means, landlord has to repair EVERYTHING that is related to habitability of the unit, free of charge.  In case when tenant damaged something, the landlord still has to repair it, but the expense can be passed to the tenant.  In all other cases when thing broke (wear and tear, theft, crime, etc), the landlord has to repair and cover the cost themselves. 

Home warranty is what seller offers to the buyer.  It is not applicable in the case of landlord/tenant.  Home warranty usually include a charge (e.g. $50-70) per visit.  The tenant should not pay this charge.