Hello @ElleneC ,
For the sake of visibility I wanted to provide the email response that was sent to you by the API team.
Thank you for reaching out to Constant Contact API Developer Support. I'm sorry but Constant Contact is unable to directly integrate with Squarespace at this time but that is a feature we're looking into implementing, we just don't have a time frame when it would be available. There are however options to connect Constant Contact to Squarespace. If you're looking to add a sign-up form to your website, below is documentation on how to add an in-line form to your website.
If you're looking for a feature where contacts are added to your account after making a purchase for instance, we use a 3rd party service called Zapier which will bridge Squarespace to Constant Contact allowing contacts to be added to your account. Below is document on how to view and connect Zapier integrations.