Technically It can, but only under carefully controlled laboratory conditions. If we're talking about the way water drains in a sink or toilet, then this is just an urban myth.
The rotation of water in things such as a sink or toilet can be explained by angular momentum or simply by the design of the bowl.
The most observed example of this effect is the motion of winds and seas on Earth. The effect is caused by the rotation of the earth, but as our planet only rotates once per day the Coriolis effect is quite small and can only be observed by motions over vast distances. Hence why this effect does not affect the way in which water drains, but does have an affect on the more substantial movements of water on Earth.