Can I require that employees take vacation time only after they've earned it?

Yes, employers are not required to permit employees to take vacation in advance of earning it.

If an employer does allow an employee to use vacation prior to it being earned, it should be treated as an advance on wages or an unsecured loan. The prudent employer will have the employee sign an agreement in writing that unearned vacation pay has been advanced to the employee which will be deducted against future accrual. However, if the employee leaves employment prior to it being earned, the value of the remaining unearned vacation pay that was advanced may not be deducted from the employee's final pay.