Sun tanning rays are called ultraviolet light (UV) and yes they can penetrate water. Within UV light, there is a spectrum of colour called the electromagnetic spectrum. The different colours within UV light can penetrate different depths, but generally the colours at the higher end of the spectrum, penetrate deepest. The blue wavelength of UV light can penetrate down to depths of 200 feet. This is said to by why deep water appears bluish.
As you can see these are small numbers. That means that UV can certainly penetrate water (especially UVA). Blue light (around 380 – 400 nm) very easily goes through water, as Sarah says. However the colour of deep water can also be affected by other things, such as marine life, dissolved chemicals and other factors.