Perturbation calculation of the axial anomaly of Ginsparg-Wilson fermion

We evaluate the axial anomaly for the general Ginsparg-Wilson fermion operator $D=D_c(\text{Id}+R{D}_c{)}^{-1}$ with $R=r\text{Id}$. For any chirally symmetric $D_c$ which in the free fermion limit, is free of species doubling and behaves like $i{\gamma }_{\mu }{p}_{\mu }$ as $p\to 0$, the axial anomaly $\text{tr}[{\gamma }_5(RD)(x,x)]$ for U(1) lattice gauge theory with single fermion flavor is equal to $e^2/(32 \pi^2) \epsilon_{\mu\nu\lambda\sigma} F_{\mu\nu}(x) F_{\lambda\sigma}(x+\hat\mu+\hat\nu)$ plus terms which are higher orders and/or non-perturbative contribtuons. The $F\tilde{F}$ term is r-invariant and has the correct continuum limit.