In this we can see how to make the google reCAPTCHA v2 as responsive for mobile devices.Thats very simple

Just add the below style code in your css

@media screen and (max-width: 575px) { 
#rc-imageselect, .g-recaptcha 
{
transform:scale(0.77);
-webkit-transform:scale(0.77);transform-origin:0 0;
-webkit-transform-origin:0 0;
} 
}