For upcoming Magento 2.x versions, Magento has planned to include this reCACPTCHA inside the package but what about the stores that are currently running in Magento 1.x? But you can use this small piece of code that will help you to Install Google reCACPTCHA on your Magento store custom form.
Read this complete here: https://magecomp.com/blog/install-google-recaptcha-magento-custom-form/
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