It would be a debit payment - I don't know of any processor that would approve a merchant account for debiting
MCA Payments - If it was possible, then this solution would work:

Authvia® TXT2PAY®


This trusted conversational commerce platform allows merchants to request and approve payments via text
without additional apps or passwords. Upon successful payment the consumer is texted a receipt, and the
merchant has transactional and conversational history as part of the consolidated reporting in the
Portal. Authvia TXT2PAY is an easy way to add a convenient, fast, and secure payment acceptance channel.

*Eliminates the need for a customer to disclose their credit card information over the phone or via email.
**Reduces the possibility of a charge-back - The transaction is a customer "push" vs. a merchant "pull"

Short Video Demo

https://vimeo.com/829129011