Heat the bloody mary mix in a saucepot until hot, 3 to 5 minutes. Add the gelatin, then whisk to combine. Allow to cool slightly, then add the vodka and stir to combine.
Trim the celery sticks so they fit side-by-side in a casserole dish, then lay them flat with the curved side facing up. Pour the mixture over the celery, trying to keep as much of it inside the celery cavities as possible. Refrigerate until firm, at least 2 hours.