Not by just squeezing some glue into the opening of the joint! Many people try this, but it is only a temporary fix at best. It will certainly fail in no time. The best (and only) way to properly glue a loose joint on a chair or any item is to take the item apart as much as possible, clean the old glue off the wood and apply fresh wood glue. The joint should be clamped fairly tightly to close the joint up for the strongest possible repair. Chairs can be very challenging to re-glue since all the joints are interdependent and it can be both time-consuming and difficult to take the chair apart without additional breakage.
If the job is too much for you please contact us and we can do it for you the proper way.