No. Customer sends Stripe their CC number, via AJAX in the browser. Acme, Inc. never has it even transiently. Stripe return a token to the browser, which is sent in a POST to Acme, Inc., then they verify it server side with a private API key.

Edit: yes Stripe has your number, but since their sole business is about securing that information, they probably do a better job of it than your typical online merchant.