  We present an intrinsic leptogenesis mechanism in models of axion inflation
with a classical SU(2) gauge field. The gauge field is coupled to the axion
with a Chern-Simons interaction and comprises a tiny fraction of the total
energy, $\frac{\rho_{_{\rm YM}}}{\rho_{_{\rm tot}}}\lesssim\epsilon^2$.
However, it has spin-2 fluctuations which breaks the parity and leads to the
generation of chiral gravitational waves during inflation. By the gravitational
anomaly in SM, it naturally creates a net lepton number density, sufficient to
explain the matter asymmetry. We show that this mechanism can generate the
observed value of baryon to photon number density in a natural range of
parameters and yet has a small chiral tensor power spectrum on large scales.
