Suppose we have some Django REST framework view with POST method which receives g_recaptcha_response key in post data, we can use request module to easily verify reCAPTCHA:

def post(self, request):
    g_recaptcha_response = request.data['g_recaptcha_response']
    r = requests.post(settings.GR_CAPTCHA_URL, {
        'secret': settings.GR_CAPTCHA_SECRET_KEY,
        'response': g_recaptcha_response
    })
    if not json.loads(r.content.decode())['success']:
        return response.Response(status=HTTP_400_BAD_REQUEST)

    # Captcha is ok do what you need and return good response

In settings.py define next constants:

GR_CAPTCHA_URL = "https://www.google.com/recaptcha/api/siteverify"
GR_CAPTCHA_SITE_KEY = "COPY FROM reCAPTCHA SITE"
GR_CAPTCHA_SECRET_KEY = "COPY FROM reCAPTCHA SITE"

Vue.js example how to generate g_recaptcha_response is here: https://hinty.io/ivictbor/recaptcha-with-vue-js-example/

Image for a hint