  We show that locally acyclic cluster algebras have (at worst) canonical
singularities. In fact, we prove that locally acyclic cluster algebras of
positive characteristic are strongly F-regular. In addition, we show that upper
cluster algebras are always Frobenius split by a canonically defined splitting,
and that they have a free canonical module of rank one. We also give examples
to show that not all upper cluster algebras are F-regular if the local
acyclicity is dropped.
