No there is no way to distribute ready-made apps to other users of non-jailbroken iOS devices without a paid Apple developer account.
If your target is jailbroken devices the answer is different.
Similarly, as @BeauNouvelle points out, if your target is other developers, you can post your source code to a site like Github and others can build the app.
You could also partner with a licensed developer who could post the app for you. If the app is a public-service type app you could likely find a developer willing to do so. You would have to give them the source and other project files and they would build the app. If you go this route, set up the licensing such that the other dev is not allowed to charge for it, and ownership remains with you. You'd also want an NDA in place to protect your intellectual property rights.