This is possible via tokenized payments by means of Sage Pay, PayPal Adaptive, or Authorize.Net CIM payment plug-ins.
Tokenization is a technology that replaces a credit card number with a token in a transaction. The token is supposed to prevent the theft of the credit card number during transmission and storage of a transaction. Tokenization simplifies the requirements of the PCI DSS, as system that no longer stores or processes sensitive data is removed from the scope of the PCI audit.
Here are Feature Requests for other payment plug-ins:
PBAS-28862 - Tokenize ePDQ payments PBAS-29121 - Tokenize Ogone payments