Will my homeowners policy pay for floor joists rotted by an unknown cause? There is also mold (mostly old) so there has been moisture at some point in time.

Wood rot of floor joists is typically not covered by a homeowner policy unless it can be tied directly to a covered event.

Typical home insurance policies provide coverage for damage that is “sudden and accidental.” For example, the accidental discharge or overflow of water from a household appliance is a peril covered by most homeowner policies. 

Thus, if a pipe burst and caused water damage to your floor joist, then at the time of the damage you likely could have made a claim.  Instead, it appears that the rot isn’t caused by a certain event but as a result of aging materials and perhaps poor maintenance.

For the mold to be covered, it also would have to be associated with a covered peril, like a burst pipe.  Mold caused by water due to condensation, excessive humidity or flooding is typically excluded from coverage provided by a home insurance policy.  (See “Mold coverage hard to find in home insurance policies.”)