Contact the manufacturer for a replacement swivel part. You may be able to get it from a hardware shop, but it will help if you know the make and model of your chair. Some chairs require specific replacement parts, so it will be easiest to contact the manufacturer or consult the instruction manual to find out which part you will need. This will save you from buying a swivel part that doesn't fit. You can also inspect your current swivel part and compare it to others in the hardware shop and select the one that matches best.
Place the rocker on its side with the back rest on the floor. Use your hand to push down on the lock system and unhook the base of the rocker to remove the swivel part. Use a screwdriver to unscrew the swivel if it is connected to the base with screws. This will detach the swivel from the base of the chair.
Inspect the swivel to see where the breakage is. The clips on the swivel commonly break, so be sure to inspect the clips as well. Broken clips will prevent the swivel action on the chair. Use the pry bar to twist and pry off the swivel part.
Apply lubricant if the swivel appears to be intact. It may be that the swivel is in good condition and simply requires lubricant to loosen up the swivel movement.
Insert the screwdriver tip into the base and hammer the clips. The hammer will pop out the clips. Ensure that all the clips are removed from the base of the rocker.
Find the clips that came with your swivel replacement package. Twist the caps onto the base and hammer the clips with a hammer or rubber mallet to secure them in place.
Position the swivel on the clips and attach the swivel to the base of the chair. Set the chair in the upright position and test out the swivel action by guiding the chair with your hand to the right and to the left.
Apply a dab of lubricant to the chair swivel if necessary.
Test out the rocker to ensure that the swivel is working properly. Sit in the chair and swivel while in it.