Yes. Stripe has been audited by a PCI-certified auditor, and has in turn been certified as a PCI Level 1 Service Provider, the most stringent level of certification available. You can confirm Stripe’s certification in Visa’s registry of service providers. Stripe is also a participant in the PCI Security Standards Council.
P-C-What? I don’t know what that means!
Payment Card Industry (PCI) security standards are minimum requirements for protecting your customers' payment card information. Adopted by Visa, MasterCard, American Express, Discover Card, and JCB, PCI compliance is required for all merchants that store, transmit, or process payment card information. Stripe’s Level 1 certification means that you can trust them with your and your customer’s financial data.