PUT /categoriasLoja/{idLoja}/{idCategoria}

curl    

 curl -X POST "https://bling.com.br/Api/v2/categoriasLoja/{idLoja}/{idCategoria}/json/"
      -d "apikey={apikey}"
      -d "xml={xml_do_vinculo_categoria}"

PHP

$url = 'https://bling.com.br/Api/v2/categoriasLoja/{idLoja}/{idCategoria}/';
$xml = '...';
$posts = array (
    "apikey" => "{apikey}",
    "xml" => rawurlencode($xml)
);
$retorno = executeUpdateCategoriesStore($url, $posts);
echo $retorno;
function executeUpdateCategoriesStore($url, $data){
    $curl_handle = curl_init();
    curl_setopt($curl_handle, CURLOPT_URL, $url);
    curl_setopt($curl_handle, CURLOPT_POST, count($data));
    curl_setopt($curl_handle, CURLOPT_POSTFIELDS, $data);
    curl_setopt($curl_handle, CURLOPT_RETURNTRANSFER, TRUE);
    $response = curl_exec($curl_handle);
    curl_close($curl_handle);
    return $response;
}

C#

public static void ExecuteUpdateCategoriesStore() {
    HttpWebRequest request =
        (HttpWebRequest)WebRequest.Create("https://bling.com.br/Api/v2/categoriasLoja/{idLoja}/{idCategoria}");
    ASCIIEncoding encoding = new ASCIIEncoding();
    string postData = "apikey={apiKey}&xml={xml_do_vinculo_categoria}";
    byte[] data = encoding.GetBytes(postData);
    request.Method = "POST";
    request.ContentType = "application/x-www-form-urlencoded";
    request.ContentLength = data.Length;
    using (Stream stream = request.GetRequestStream())
        stream.Write(data,0,data.Length);
    HttpWebResponse response = (HttpWebResponse)request.GetResponse();
    string responseString = new StreamReader(response.GetResponseStream()).ReadToEnd();
    Console.Out.WriteLine("Response Body: \r\n {0}", responseString);
}