We argue that in order to study the magneto-transport in a relativistic Weyl fluid, it is needed to take into account the associated quantum corrections, namely the side-jump effect, at least to second order. To this end, we impose Lorentz invariance to a system of free Weyl fermions in the presence of the magnetic field and find the second order correction to the energy dispersion. By developing a scheme to compute the integrals in the phase space, we show that the mentioned correction has non-trivial effects on the thermodynamics of the system. Specifically, we compute the expression of the negative magnetoresistivity in the system from the enthalpy density in equilibrium. Then in analogy with Weyl semimetal, in the framework of the chiral kinetic theory and under the relaxation time approximation, we explicitly compute the magneto-conductivities, at low temperature limit (T ≪ μ). We show that the conductivities obey a set of Ward identities which follow from the generating functional including the Chern-Simons part.