I'm not sure if he's ever been depicted as doing so in the current series. [EDIT: Yes he has, thanks to Gallifreyan] However, he was shown doing so in Ep1 of the 1990 series.
Regardless of whether he has been shown as doing so or not, it is extremely likely that he can based on real world physics and examples. The Basicliscus Lizard can run on water
...at a velocity of 1.5 meters (4.9 feet) per second for approximately
4.5 meters (15 feet)...
It is calculated here that to run on water you would have to run at approximately 30m/s, or around three times faster than Usain Bolt. Is the Flash more than three times faster than the Lightning Bolt? The Flash has been depicted as running at at least Mach 1 which is 343 m/s.
So yes, the Flash could run on water.