Yes, with Manifold Pay pay by link. From the invoice's Collect Payment section you text, email or copy the customer a secure link. They pay by card on their own phone or computer, and the payment records itself on the invoice within a few minutes. Pay by link has to be connected first, under Settings > Payments. See "Sending a customer a pay link" and "Setting up pay by link".
To take a deposit when a customer approves an estimate, use Send for Approval instead. See "Sending an estimate to a customer for approval".
If you take cards on another processor that sends customers its own pay links, those payments are not recorded automatically. Record each one on the invoice as External Card once it clears.