You would usually say "Splashed me with water/dirty water", but my usual response to that kind of thing happening would be many swear words intended for the driver of the car..

The car splashed dirty water all over me.

You could say.. "The car splattered dirty water on me." " The car splashed dirty water on me."

Cześć Izabela, Yes, you can say a car splashed you.. but the common preposition is "with".. Example: A car splashed me with muddy water! ... When describing the resulting stains, you can use the verb spatter.. The mud spattered my clothes and boots.

You can say the car “splattered you with…” instead!