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Reciprocity, in the context of optics and scattering, is defined as invariance when a source and detector are swapped indicating that the motion of an object in one direction being the same as that in the opposite. We investigate the magnetic field tuning of non-reciprocal spin waves in antiferromagnetic langasite Ba₃NbFe₃Si₂O₁₄ using neutron spectroscopy. Applying a time reversal symmetry breaking magnetic field that also breaks a two-fold symmetry of the underlying structure, different spin wave energies are observed when the sign is reversed for either the total momentum +/- Q=+/-(G +/- q) or applied magnetic field +/- μ₀H. We discuss the scaling of this effect with field and suggest it microscopically originates from spin-orbit coupling mediated through antisymmetric exchange.