1. Create a textbox control on the form or view and set its Name property to "txtReturnValue" and uncheck its Visible property.
2. Create a data label control on the form or view and set its Expression property to the following, replacing the sitekey attribute's value with your reCAPTCHA Google api site key:
<script type="text/javascript">var recaptchaCallback = function(response) {$('input[name="txtReturnValue"]').trigger("focus").val(response).trigger("blur");};</script><script src='https://www.google.com/recaptcha/api.js' ></script> <div class="g-recaptcha" data-sitekey="your-google-recaptcha-sitekey" data-callback="recaptchaCallback"></div>
3. Create one or more Changed Event rules on the txtReturnValue control to implement the logic that only allows the form from being submitted when the reCaptcha has been successfully processed. For example you could enable the Submit button which has is disabled by default.
4. In addition to or as an alternative, add conditions to any rules on form buttons controls to check the txtReturnValue control has a value. For example, only perform the desired actions on the Submit button when the txtReturnValue control has a value.
Google's api responds with a long string value when the user has successfully validated they are not a robot. What the value is that is put into the txtReturnValue textbox doesn't matter, just don't allow the users to access or view that control.