I've done this with various woods but not oak. However I understand oak has a fairly high tannin content so give it a go.
Take old nails and ferrous metal screws, the older the better. Put 'em in a jar of water for a week or so to get nice and rusty. On the day of the treatment make a good strong brew of tea, preferably leaf tea but teabags will do. Paint the wood with a coating of cold tea then, while the wood is still damp, coat with the rusty liquor from the nails. The wood will go dark from the reaction between the Fe and the tannin. More coats will make the wood black as soot.
It works and it's free (almost).