It doesn't on any of the games, and you can't teach it to him/her with a
TM either. To find out the answer to questions like this one and many more look up serebii.net
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Sandslash learns Dig at level 30 in Pokemon X and Y. In Pokemon Omega Ruby and Alpha Sapphire, it can learn Dig at level 33.
If you level it up to level 45 you will be able to let it learn dig, but remember you'll have to delete a move to learn it.
Dig is a TM, so you can teach it to it at any level.
Get relicanth and wailord. Put relicanth in the first slot and the wailord in the last. Then make a pokemon who has dig use dig.
At level 40 it will want to learn dig