In this paper we prove uniqueness for an inverse boundary value problem for the magnetic Schr\"odinger equation in a half space, with partial data. We prove that the curl of the magnetic potential A, when A∈W1,∞comp(\ov\R3−,\R3), and the electric pontetial q∈L∞comp(\ov\R3−,\C) are uniquely determined by the knowledge of the Dirichlet-to-Neumann map on parts of the boundary of the half space.