Summary: \(D\)-branes have a world-volume \(\operatorname{U}(1)\) gauge field \(A\) whose field strength \(F = d A\) gives rise to a Born-Infeld term in the \(D\)-brane action. Supersymmetry and kappa symmetry transformations of \(A\) are traditionally inferred by the requirement that the Born-Infeld term is consistent with both supersymmetry and kappa symmetry of the \(D\)-brane action. In this paper, we show that integrability of the assigned supersymmetry transformations leads to an extension of the standard supersymmetry algebra that includes a fermionic central charge. We construct a superspace one-form on an enlarged superspace related by a coset construction to this centrally extended algebra whose supersymmetry and kappa symmetry transformations are derived, rather than inferred. It is shown that under pullback, these transformations are of the form expected for the \(D\)-brane \(U(1)\) gauge field. We relate these results to manifestly supersymmetric approaches to construction of \(D\)-brane actions.