Hi @nora-mcdougall,
Thanks for contacting me here.
Right now, AWPCP supports PayPal, Stripe, 2Checkout and PayFast for payment gateways. Square’s API is a possibility for the future, although we don’t support it today. Features like that are based on user demand, and yours is the first request we’ve had specifically for Square.
We probably won’t get to it for a bit, because we’re currently revamping the plugin to be a full custom post type (long overdue) and are close to being beta-ready. Once that work is finished, we can consider what steps to take next.
Please let me know if you have any other questions or issues!