The scaling of antiferromagnetic ordering temperature of corundum-type chromia films has been investigated. Néel temperature TN was determined from the effect of perpendicular exchange bias on the magnetization of a weakly-coupled adjacent ferromagnet. For a thick-film case, the validity of detection is confirmed by a susceptibility measurement. Detection of TN was possible down to 1-nm-thin chromia films. The scaling of ordering temperature with thickness was studied using different buffering materials and compared with Monte-Carlo simulations. The spin-correlation length and the corresponding critical exponent were estimated, and they were consistent between experimental and simulation results. The spin-correlation length is an order of magnitude less than cubic antiferromagnets. We propose that the difference is from the change of number of exchange-coupling links in the two crystal systems.