Repairing a wobbly dining chair instead of replacing the set

One dining chair rocks even on a level floor. Looking underneath, a corner joint has opened slightly; the wood itself isn't split. I can wiggle the side rail by hand. I'm reluctant to drive screws through the frame just to make it feel tight for another month. Is the proper repair to separate the loose joint, clean the old glue and reclamp it? The other chairs are fine, and replacing the whole set would be ridiculous.