No, fish drink fluids from the surrounding environment. This includes the water from other sources such as rain and puddles.
Many people make a common mistake in thinking that fish themselves drink water when they really don't. Fish absorb all their fluids directly into their body through tiny holes around their mouth called gills. These gills have special blood vessels called capillaries that help draw in the necessary "drinking" fluid while extracting oxygen for respiratory use. In a sense, these fishes can never get thirsty because they never ingest liquid to excrete it again- they simply use what's given to them by the world around them through which they swim!