Yes, you can accept most internationally-issued cards bearing the Visa, MasterCard, American Express, Discover, JCB, or UnionPay logo.

From our support article, a couple tips to keep in mind when manually processing these cards:

• To switch between numbers and letters on your device:
  • iOS: Tap ABC or 123 at the lower left of the screen 
  • Android: Tap the keyboard icon to the right of the payment card field
• If you experience issues processing an internationally-issued card, have the cardholder contact their issuer. 
• Cardholders may be charged for currency conversion by their card issuer since payments must be processed in your country's official currency.
• You must be located in the country where you activated your Square account to process payments.