Per SFGATE, California is now a "right to dry" state after Gov. Jerry Brown signed a bill Thursday restricting homeowners associations from banning clotheslines, which the groups deemed unsightly additions to neighborhoods.

The article, Brown signs bill reversing bans on clotheslines - SFGate, makes it clear that renters have those rights.
Now, the law states landlords must allow tenants to air-dry their clothes in their own backyard if they wish, as long as "the clothesline or drying rack will not interfere with the maintenance of the rental property and the use of the clothesline or drying rack does not violate reasonable time or location restrictions imposed by the landlord."