{
  "return_code":0,
  "return_message":"",
  "result":{
    "store_key":"ab37fc230bc5df63a5be1b11220949be"
  }
}

index.php

<?php

include_once 'Connector.php';

$api = new Connector('PASTE_YOUR_API_KEY');

$params = array(
  'cart_id'      => 'BigcommerceApi',
  'store_url'    => 'http://example.com',
  'verify'       => 'false',//set this param=false for test only
  'store_key'    => 'ab37fc230bc5df63a5be1b11220949be',
  'AdminAccount' => 'admin',
  'ApiPath'      => 'http://example.com/api/v1',
  'ApiKey'       => '6b89704cd75738cb0f9f6468d5462aba',
);

try {

  /**
   * Return stdClass
   */
  $result = $api->request('cart.create', $params);

  echo 'Store Key: ' . $result->store_key;

} catch (Exception $e) {

  echo '#' . $e->getCode() . ' ' . $e->getMessage();

}

Connector.php

<?php

/**
 * Class Connector
 */
class Connector
{
  /**
   * URL to API API2Cart
   *
   * @var string A2C_URL
   */
  const A2C_URL = 'https://api.api2cart.com/v1.0/';

  /**
   * @var array $_params
   */
  private $_params = array();

  /**
   * @param string $apiKey
   * @param string $storeKey
   */
  public function __construct($apiKey, $storeKey = null)
  {
    $this->_params['api_key']   = $apiKey;

    if($storeKey !== null) {
      $this->_params['store_key'] = $storeKey;
    }
  }


  /**
   * Send request to API2Cart
   *
   * @param string $method Name method
   * @param array  $params List params for method
   *
   * @return stdClass
   *
   * @throws Exception
   */
  public function request($method, $params = array())
  {

    $params = array_merge($this->_params,$params);

    $ch = curl_init();

    $url = self::A2C_URL . $method . '.json?' . http_build_query($params);

    curl_setopt($ch, CURLOPT_URL, $url);
    curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, true);
    curl_setopt($ch, CURLOPT_HEADER, false);
    curl_setopt($ch, CURLOPT_TIMEOUT, 300);
    curl_setopt($ch, CURLINFO_HEADER_OUT,true);
    curl_setopt($ch, CURLOPT_RETURNTRANSFER, 1);
    curl_setopt($ch, CURLOPT_USERAGENT, 
      "Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; " .
      "rv:1.8.1.1) Gecko/20061204 Firefox/2.0.0.1");
    curl_setopt($ch, CURLOPT_HTTPHEADER, array (
      "Accept: */*",
    ));

    try {

      $response = trim(curl_exec($ch));

      if(curl_errno($ch) != CURLE_OK) {
        throw new Exception(curl_error($ch));
      }

      curl_close($ch);

      return $this->validate($response);

    } catch (Exception $e) {

      throw $e;

    }
  }

  /**
   * Validate received response
   *
   * @param string $response Response
   *
   * @return stdClass
   *
   * @throws Exception
   */
  private function validate($response)
  {
    $result = json_decode($response);

    if($result === null) {
      throw new Exception('Response NULL');
    }

    if($result->return_code != 0) {
      throw new Exception($result->return_message, $result->return_code);
    }

    return $result->result;
  }
}