  The one-loop QCD effective charge $\alpha_s^{eff}$ for quark-quark scattering
is derived by diagrammatic resummation of the one-loop amplitude using an
arbitary covariant gauge. Except for the particular choice of gauge parameter
$\xi = -3$, $\alpha_s^{eff}$ is found to {\it increase} with increasing
physical scale, $Q$, as $\ln Q$ or $\ln^2 Q$. For $\xi = -3$, $\alpha_s^{eff}$
decreases with increasing $Q$ and satisfies a renormalisation group equation.
Also, except for the case $\xi = 19/9$, convergence radii of geometric series
are found to impose upper limits on $Q$.
