Definitely, @mirab327! You can send your customer a secure form to fill out their credit card information, which will then be kept on file.
Rest assured, with the highest level of data security and privacy, this sensitive information won't be viewable or printable. This way, you can confidently manage customer transactions while safeguarding their personal details. Allow me to give you a brief summary of this service and its key features.
With QuickBooks Online, you can send customer invoices and integrate them using QuickBooks Payments, which allows customers to see a button to pay their invoices or you can send payment links. The customers will have to fill out this type of form, however, this only allows them to make invoice payments without re-entering card information. Please check my snippets below:

Once a customer clicks the View and pay button, they can fill out their credit card data. Take note that this is exclusive to US-based customers only.

An alternative solution to charge customer credit cards for manually handling invoices, I kindly recommend reaching them out directly for their permission and required information. This way, you can enter their details in QuickBooks Payments and use other methods to process payments such as charging a card, processing e-checks, and capturing funds. Allowing you to charge customer cards after invoicing them.
To learn more about it, you can sign up for QuickBooks Payments to process customer payments in QBO with QuickBooks Payments.
In addition, your customer can also use the Autopay feature to pay recurring invoices. I'd like you to check this article: Set up Autopay for recurring invoices in QuickBooks Online. To avoid missing out on any unpaid customer invoices, you can easily send a customer statement. Take a look at this article: Create and send customer statements.
Thank you for reaching out. I hope this information helps you process customer credit card payments in QuickBooks Online. If you have any further questions or need additional assistance with customer payments, or anything else related to QuickBooks, please don't hesitate to let me know. I'm here to help and more than happy to support you with any queries. Have a great day, mirab327!