It is an old quick&dirty method to soak axe handles in a bucket of water when the head isn't tight anymore. However, this will not be anything but a temporary measure as handles thus treated tend to shrink even more when the water has evaporated.
A common advice on what to do instead is to soak the handle in linseed oil. This is a good idea to prevent the handle from shrinking in the first place, but won't usually swell the handle enough to end the wiggle.
What will work is glycerol. It is hygroscopic, meaning it attracts moisture. So after it has soaked into the wood, it will attract moisture, swelling it. In the US you can get Swel-Lock, which is most likely glycerol based (+ something that makes it a little less viscous and thus better penetrating).
Ookami
A common advice on what to do instead is to soak the handle in linseed oil. This is a good idea to prevent the handle from shrinking in the first place, but won't usually swell the handle enough to end the wiggle.
What will work is glycerol. It is hygroscopic, meaning it attracts moisture. So after it has soaked into the wood, it will attract moisture, swelling it. In the US you can get Swel-Lock, which is most likely glycerol based (+ something that makes it a little less viscous and thus better penetrating).
Ookami