Can I refund a customer as store credit instead of money?

Yes, with the Wallet / Store Credit plugin, which gives each customer a wallet they can spend at checkout.

• To give store credit for a return, open the customer in the plugin's Customer Wallets tab and use Manual adjustment → Credit, with a reason.
• Anything the customer originally paid from their wallet goes back to it automatically when the whole order is cancelled or refunded.

A return ends in Refunded, Exchanged or Cancelled, or Return Rejected if you decline it.