  The elastic $\alpha$-$^{12}$C scattering for $l=0,1,2,3$ channels at low
energies is studied, including the energies of excited bound states of
$^{16}$O, in effective field theory. We introduce a new renormalization method
due to the large suppression factor produced by the Coulomb interaction when
fitting the effective range parameters to the phase sift data. After fitting
the parameters, we calculate asymptotic normalization constants of the $0_2^+$,
$1_1^-$, $2_1^+$, $3_1^-$ states of $^{16}$O. We also discuss the uncertainties
of the present study when the amplitudes are interpolated to the stellar energy
region of the $^{12}$C($\alpha$,$\gamma$)$^{16}$O reaction.
