Pull the leg rung out of the chair frame if possible. The frame usually has some give to it so carefully separate the legs to slide the rung out. Once the legs are slightly further apart, slip one side of the rung out from where it connects and then pull the other side loose. This allows you to more efficiently remove the old glue on the rung and tighten it more effectively. If the rung is broken completely, pull it out so a replacement can be glued and inserted. Be careful to not break the frame by pulling the legs apart too hard.
Scrape the ends of the rungs off with a razor to remove any old glue or adhesive.
Apply fresh glue to both ends of the rung and reinsert it into the chair frame. Wipe away excess glue with a rag. Put a clamp over both ends of the rung to hold it firmly in place while it dries. Use a filling epoxy if the rung is loose in the socket because the epoxy hardens to help fill the extra space in the frame.