  We calculate the $O(\alpha_s)$ and $O(\alpha_s^2)$ gluon radiative
corrections to the QCD sum rule for the first Gegenbauer moment $a_1^K$ of the
kaon light-cone distribution amplitude. The NNL0 accuracy is achieved for the
perturbative term and quark-condensate contributions to the sum rule. A
complete factorization is implemented, removing logarithms of $s$-quark mass
from the coefficients in the operator-product expansion. The sum rule with
radiative corrections yields $a_1^K(1 \GeV)=0.10\pm 0.04$.
