If you would like to add reCAPTCHA to an embedded Drip form, go to the embedded form in your Drip account that you wish to enforce with reCAPTCHA, and scroll down until you see where you'll enter your "Site Key":
Follow the instruction to set up your API key pair from Google. Once you have registered your website and received your API key pair, enter those credentials into the form fields and click the Save button.
You should now have a similar view as this screenshot below:
Copy and paste the updated form code and add the provided script to your website. Be sure to tick the Enable recaptcha for this form checkbox as specified in the instructions. You will now have an embedded Drip form complete with reCAPTCHA to protect your subscriber segments from acquiring any nasty bots!