The renormalization group analysis is applied to the high-energy behavior of the pion form factor in QCD. The anomalous dimension of the form factor is directly related to the short-distance behavior of the Bethe-Salpeter wave function with suitable choice of normalization. Absence of infrared singularities and short-distance dominance are proven by the use of a power counting argument in the axial gauge. The relation between our method and the "factorization" method is clarified. The applicability of our method to other elastic form factors is discussed.