  We show that the dimer algebra of a connected Postnikov diagram in the disc
is bimodule internally 3-Calabi-Yau in the sense of the author's earlier work.
As a consequence, we obtain an additive categorification of the cluster algebra
associated to the diagram, which (after inverting frozen variables) is
isomorphic to the homogeneous coordinate ring of a positroid variety in the
Grassmannian by a recent result of Galashin and Lam. We show that our
categorification can be realised as a full extension closed subcategory of
Jensen-King-Su's Grassmannian cluster category, in a way compatible with their
bijection between rank 1 modules and Pl\"ucker coordinates.
