I wonder if you can do it through the "send data to another website" function - you would need the API keys or whatever information is required, for that from Square itself.
https://docs.machform.com/help/sending-form-data-to-another-website
Suggest to ask further help from Appnitro through their ticket support as the forum here is not for official support.
Do you mean you want it to interface with the credit card reader hardware, or just accept payments online through a web form as per typical methods?