No, Stripe doesn’t integrate with PayPal — we currently support credit and debit card payments.
Don’t take my word for it. Patrick Collison – who happens to be one of the co-founder of Stripe – used these exact words. In fact those are his words https://www.quora.com/Can-customers-pay-with-PayPal-via-Stripes-API/answer/Patrick-Collison
The fact is that PayPal and Stripe both serve the same purpose and that is processing debit and credit card payments. Merchant Maverick gets into much more detail on this comparison.
I speak to people all the time that ask me if they can integrate PayPal with Stripe. I think that these people might be confused by the nice popup overlay that is used by Stripe Checkout – one of the products offered by Stripe – to accept payment information such as name, address and credit card number, etc.
At this time, inserting additional payment processors functionality such as PayPal into this popup is not an option and would not make much sense for Stripe since they want to process the payment for you. If this is something that you really want, one option would be to build your own custom popup overlay from scratch using Stripe.js – another one of Stripes products.
This would obviously require more development work but you could accomplish what appears to be Stripe and PayPal integration although in reality you are simply offering both payment types independent of one another on the same page or form. An example of this type of implementation can be found at the Khan Academy Donation page.
Zapier appears to offer some level of integration but it is not 100% clear from this page how this works.