Well, yes, drinking water can reduce the wrinkles under your eyes. Generally speaking, you should drink between 8 and 10 glasses of water each day. And drinking water can do a good job to your eyes. For example, by drinking water, it makes your eyes and mouth moist. In that way, it can just relieve your wrinkles under your eyes. On the other hand, it washes dirt and dust right from your eyes. And in this way, it can decrease the risk you get the dry eyes. Also, water is not only good for your eyes, but also for your other parts of your body, such as the brain, the cells, and the organs. For example, Drinking water is like oiling your body's joints. Anyway, just drink more water.
Actually drinking suitable amount of water will be helpful for your eye wrinkles because of the moisture role. However, drinking large amount of water will make you get the swollen eyes, especially drinking large amount of water before the sleep. If you want to reduce the eye wrinkles, you could use the oil essentials to help you which will be so useful.
Well, as a matter of fact, eye wrinkles is a sign of aging, which could not be reversed in a natural way, unless you try to get some plastic surgery, but that could have some side effects anyway. So, you mentioned water, and I know well water is essential to our skin and health but it is not that powerful, maybe proper amount of water could make your skin more moist, but you could not relieve those eye wrinkles. Maybe you should use some cosmetics.