This is the English rendering of a Latin saying of Ovid the poet, but it is used:
Dripping water hollows out stone, [not through force but through persistence].
― Ovid (GoodReads)
OxfordReference gives this variant:
constant dropping wears away a stone
and explains that the saying was:
primarily used to mean that persistence will achieve a difficult or unlikely objective (in the US, continual is often used for constant). The saying is recorded from the mid 13th century, but a similar thought is found in classical Greek, in the Fragments of Choeriuls of Samos,
with persistence a drop of water hollows out the stone,
and in Latin, in the Elegies of Tibullus,
length of time eats away stones with soft water.
This is also listed in the Farlex Dictionary of Idioms quoted by Free Dict:
constant dripping wears away a stone
Success is earned through persistence and determination.
- My swing only got better after I started practicing it every day, so I guess it's true that constant dripping wears away a stone.
I suspect it appeared in Russian from the same ancient sources.
As for the most common variant, this Ngram can give you an idea:
At the end of the day, it is your choice, pick the one that fist best your taste, your side of the pond and your context.