Chiral pumping from optical electric fields oscillating at terahertz frequencies is observed in the Weyl material TaAs with electric and magnetic fields aligned along both the and axes. Free-carrier spectral weight enhancement is measured directly, confirming theoretical expectations of chiral pumping. A departure from linear field dependence of the Drude weight is observed at the highest fields in the quantum limit, providing evidence of field-dependent Fermi velocity of the chiral Landau level. Implications for the chiral magnetic effect in Weyl semimetals from the optical -sum rule are discussed.