Summary: Let \(S\) be an inverse AG-groupoid (Abel-Grassmann groupoid) and define a relation \(\gamma\) on \(S\) by \(a\gamma b\) if and only if there exist some positive integers \(n\) and \(m\) such that \(b^m\in (Sa)S\) and \(a^n\in (Sb)S\). We prove that \(S/\gamma\) is a maximal semilattice homomorphic image of \(S\). Thus, every inverse AG-groupoid \(S\) is uniquely expressible as a semilattice \(Y\) of some Archimedean inverse AG-groupoids \(S_\alpha\) (\(\alpha\in Y\)). Our result can be regarded as an analogy of the well known Clifford theorem in semigroups for AG-groupoids.