Currently DNN does not suppport Recaptcha out of the box. There is a github issue discussing this on https://github.com/dnnsoftware/Dnn.Platform/issues/4409, feel free to chime in on this discussion.
In the meantime you could use Live Forms for registration which has Recaptcha on board. And lots of other goodies. https://www.mandeeps.com/products/dnn-modules/live-forms
If you already have ActionForm (DNN Sharp) or Plant an app, these also offer the recaptcha.