Dissipationless currents from topologically protected states are promising for disorder-tolerant electronics and quantum computation. Here, we photogenerate giant anisotropic terahertz nonlinear currents with vanishing scattering, driven by laser-induced coherent phonons of broken inversion symmetry in a centrosymmetric Dirac material ZrTe5. Our work suggests that this phononic terahertz symmetry switching leads to formation of Weyl points, whose chirality manifests in a transverse, helicity-dependent current, orthogonal to the dynamical inversion symmetry breaking axis, via circular photogalvanic effect. The temperature-dependent topological photocurrent exhibits several distinct features: Berry curvature dominance, particle-hole reversal near conical points and chirality protection that is responsible for an exceptional ballistic transport length of similar to 10 mu m. These results, together with first-principles modelling, indicate two pairs of Weyl points dynamically created by B-1u phonons of broken inversion symmetry. Such phononic terahertz control breaks ground for coherent manipulation of Weyl nodes and robust quantum transport without application of static electric or magnetic fields.