Clean and tidy the arm of the chair while detached. Clean the surface with wood cleaner and a lint-free cloth. Allow the arm to dry completely. Apply wood filler into the cracks of the chair with a spatula and allow the filler to set for the time indicated by the manufacturer.
Sand down the arm of the chair with fine-grit sandpaper. Firmly massage the entire surface of the arm with the sandpaper. Apply paint or wood stain to match the original color. Apply with a paint brush and allow it to dry completely.
Polish the arm with wood polish and a clean, lint-free cloth. Apply one thin coat of polish, allow it to dry for 15 minutes, then apply a second coat.
Find the holes where the original screws connected the chair to the frame. Screw in brand new screws with a screwdriver. The older screws are most likely rusted, compromising the strength of the joint.
Fill in the cracks between the arm and the body with wood glue. If the holes where the screws exist are weakened from buildup, the wood glue will reinforce the connection. Let the wood glue dry for 24 hours before sitting in the chair and using the arm rests.