PHP – cURL

$curl = curl_init();

curl_setopt_array($curl, array(
  CURLOPT_URL => "http://my-site.com/wp-json/wpcargo/v1/api/{my_API_key}",
  CURLOPT_RETURNTRANSFER => true,
  CURLOPT_ENCODING => "",
  CURLOPT_MAXREDIRS => 10,
  CURLOPT_TIMEOUT => 0,
  CURLOPT_FOLLOWLOCATION => true,
  CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
  CURLOPT_CUSTOMREQUEST => "GET",
  CURLOPT_HTTPHEADER => array(

  ),
));

$response = curl_exec($curl);

curl_close($curl);
echo $response;

javascript – jQuery

var settings = {
  "url": "http://my-site.com/wp-json/wpcargo/v1/api/{my_API_key}",
  "method": "GET",
  "timeout": 0,
  "headers": {
  },
};

$.ajax(settings).done(function (response) {
  console.log(response);
});