Josephson current between two one-dimensional nanowires with proximity induced $p$-wave superconducting pairing is calculated in the presence of Rashba spin-orbit interaction, in-plane and normal magnetic fields. We show that Andreev retro-tunneling is realized by means of three channels. The main contribution to the Josephson current gives a scattering in a conventional particle-hole channel, when an electron-like quasiparticle reflects to a hole-like quasiparticle with opposite spin yielding a current which depends only on the order parameters phase differences $varphi$ and oscillates with $4pi$ period. Second anomalous particle-hole channel, corresponding to the Andreev reflection of an incident electron-like quasiparticle to an hole-like quasiparticle with the same spin orientation, survives only in the presence of the in-plane magnetic field. The contribution of this channel to the Josephson current oscillates with $4pi$ period not only with $varphi$ but also with orientational angle of the in-plane magnetic field $theta$ resulting in a magneto-Josephson effect. Third anomalous particle-particle channel, which represents a reflection of an electron-like (hole-like) quasiparticle to a electron-like (hole-like) quasiparticle with opposite spin-orientation, oscillates only with the in-plane magnetic field orientation angle $theta$. We present a detailed theoretical analysis of both DC and AC Josephson effects in such a system showing contributions from all these channels and discuss experiments which can test our theory.
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