Having reCAPTCHA show up AFTER email has been inputted

Site URL: http://www.camberapp.com

Hi there! I successfully added reCAPTCHA to my newsletter form so I wouldn't have to do a confirmation email, yet I'd love it to only appear after someone has entered their email. Right now, it sticks out like a sore thumb against the branding of my site :/ Is there custom code that I can input so that the reCAPTCHA box only appears after someone inputs their email?

Thanks!