Very likely yes.
I don't know what the standard lease form in Richmond provides, but the standard lease form in Northern Virginia has a check box specifying whether the tenant is to pay the water bill. And on a rental property I own--that box is checked and the renter pays the water bill.
I'm not a lawyer, so what follows isn't legal advice. However . . .
Even if a landlord didn't use the standard Realtor-approved lease, the question really would be whether it's prohibited. If Richmond prohibits it, then it wouldn't be legal. However, if Richmond is silent on the matter, then a landlord certainly could charge for water.
It can get a bit stickier if you're living in a multi-unit building and you'd be expected to pay the entire bill. Or a bit more complex if a single bill is going to be prorated among multiple tenants. Then you'd just want to make sure you were comfortable with the split, or the process by which it was determined how much you owed.
Hope that helps.