What I believe you can't do is have your own frontend send the data in the form to your own backend, then forward on to the other service from there. Once the plaintext card details touch your servers you have to be PCI compliant, even if you aren't storing them.
If you absolutely can't do the former on your frontend, eg because you don't want to use JS or something similar, then you can use services like Stripe checkout where they host the frontend on a URL you redirect to from your app, etc.