Starting from the Bogolubov-de Gennes theory describing the induced superconductivity in a curved Majorana nanowire, we analyze the effect of the wire geometry on the topologically nontrivial superconducting correlations. We show that the topological phase transition can reveal itself in the Josephson transport through a curved Majorana nanowire resulting, in particular, in specific geometry-dependent phase battery effect and magnetochiral phenomena.