Acquia\Cloud\Api\CloudApiClient::deployCode PHP Method

    public function deployCode($site, $sourceEnv, $targetEnv)
    {
        $variables = array('site' => $site, 'source' => $sourceEnv, 'target' => $targetEnv);
        $request = $this->post(array('{+base_path}/sites/{site}/code-deploy/{source}/{target}.json', $variables));
        return new Response\Task($request);
    }