Summary: In this article we establish a version of Koszul duality for filtered rings arising from \(p\)-adic Lie groups. Our precise setup is the following. We let \(G\) be a uniform pro-\(p\) group and consider its completed group algebra \(\Omega =k\llbracket G\rrbracket\) with coefficients in a finite field \(k\) of characteristic \(p\). It is known that \(\Omega\) carries a natural filtration and \(\text{gr} \Omega =S(\mathfrak{g})\) where \(\mathfrak{g}\) is the (abelian) Lie algebra of \(G\) over \(k\). One of our main results in this paper is that the Koszul dual \(\text{gr} \Omega^!=\bigwedge \mathfrak{g}^{\vee }\) can be promoted to an \(A_{\infty }\)-algebra in such a way that the derived category of pseudocompact \(\Omega\)-modules \(D(\Omega)\) becomes equivalent to the derived category of strictly unital \(A_{\infty }\)-modules \(D_{\infty }(\bigwedge \mathfrak{g}^{\vee })\). In the case where \(G\) is an abelian group we prove that the \(A_{\infty }\)-structure is trivial and deduce an equivalence between \(D(\Omega)\) and the derived category of differential graded modules over \(\bigwedge \mathfrak{g}^{\vee }\) which generalizes a result of Schneider for \(\mathbb{Z}_p\).