  We propose a new renormalization scheme of the running coupling constant in
general gauge theories using the Wilson loops. The renormalized coupling
constant is obtained from the Creutz ratio in lattice simulations and the
corresponding perturbative coefficient at the leading order. The latter can be
calculated by adopting the zeta-function resummation techniques. We perform a
benchmark test of our scheme in quenched QCD with the plaquette gauge action.
The running of the coupling constant is determined by applying the step-scaling
procedure. Using several methods to improve the statistical accuracy, we show
that the running coupling constant can be determined in a wide range of energy
scales with relatively small number of gauge configurations.
