To invoice in USD you will first need to turn on multi-currency by going to the Gear icon > Accounts and Settings > Currency > Multicurrency.
Once you have enabled this you will need to create your customer and set them to be invoiced in USD. To do this go to Sales > Customers > New customer > enter customer details and on the payment and billing tab select 'This customer pays me with' and select the currency.
When you then create an invoice with this customer selected as the payee the currency will change automatically.