  We study the scaling property of the ratio of the critical temperature $T_c$
to the square root of the string tension $\sigma$ in the SU(3) pure gauge
theory using a renormalization group improved action. We first determine the
critical coupling $\beta_c$ on lattices with temporal extension $N_t=4$ and 6,
and then calculate the static quark potential at the critical couplings on
lattices at zero temperature. The values of $T_{c}/\sqrt{\sigma}$ in the
infinite volume limit are identical within errors, while they are slightly
larger than the value extrapolated to the continuum limit with the standard
action. We also note that the rotational invariance of the static quark
potential is remarkably restored in the both cases, and that the potential
$V(R)$ in physical units scales in the whole region of $R$ investigated.
