Member registration from a 3rd party app (iOS / Android)

I need to allow members to register on one of our websites from its related app for iOS / Android.

At first I thought I’d just give the developers of the app direct access to the DB to insert records in the exp_members and exp_member_data tables, but quickly realised it’s a very bad idea, and not just from a security point of view, as it raises billions of other problems.

Then I thought I could create a simple registration page on our website for the app to connect to so that the whole registration process would actually happen on the website.

Any other ideas on how this could be achieved? Are there any plugins or something like that out there that can be used for this?

Thanks!