Yes. You can absolutely send a sick employee home, but you’ll want to make sure you’re doing so consistently for visibly-ill
employees. In fact, I would recommend having a policy to that effect and clearly communicating that policy to your employees. That way sick employees know what is expected of them and can save themselves the trip to work.
Be aware, however, that some states require reporting time pay, so if you send a non-exempt employee home before their shift starts, or before it’s over, you may still owe them a few hours of pay. And exempt employees in all states must be paid for a full day of work, even if sent home early due to illness, if any work at all was performed that day, including work from home.
Many employers find it advantageous to offer paid sick leave so that employees who are under the weather don’t have to worry about receiving a smaller paycheck and are less likely to come in and spread their germs. They can focus on getting rest and feeling better so they can return to work healthy and productive.