Google reCaptcha have 4 different standard themes from which Red theme is used by default. But reCaptcha have 3 more themes which names like, “white”, “blackglass”, “clear” You also can read more about custom styling here
To use one of standard themes you can do something like this. Edit includes/header.php and put the following code before </head>
<script type="text/javascript">
var RecaptchaOptions = {
theme : 'theme_name'
};
</script>
In code above you can change theme_name to white, red, blackglass, and clean. That will change the style of your reCaptcha style in php login and user management system. For quick note admin can activate reCaptcha in user management and login system from general_settings.php after login as admin.