Check whether the wobble is from loose closet bolts
Remove the bolt caps at the toilet base
Tighten the closet bolts evenly, alternating sides
Stop tightening if the toilet starts to crack or shift unevenly
Test the toilet for movement
If the toilet still wobbles, check for an uneven floor
Insert plastic shims under the toilet base where needed
Trim any excess shim material flush with the base
Recheck that the toilet sits level and does not rock
If the wax ring is damaged or the toilet leaks, remove the toilet and replace the wax ring
Reinstall the toilet and tighten the bolts evenly
Caulk around the base only after the toilet is stable, leaving a gap at the back if desired
Replace rusted, broken, or stripped bolts and washers
Call a plumber if the flange is damaged or the floor is rotted