Примерно так. Попробуйте, должно работать.
<?php
$url = "https://afisha.yandex.ru/export/json/";
$KEY = "xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx";
$curl = curl_init();
curl_setopt_array($curl, array(
CURLOPT_URL => $url,
CURLOPT_RETURNTRANSFER => true,
CURLOPT_ENCODING => "",
CURLOPT_MAXREDIRS => 10,
CURLOPT_TIMEOUT => 30,
CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
CURLOPT_CUSTOMREQUEST => "GET",
CURLOPT_HTTPHEADER => array(
"Authorization: Bearer" $KEY,
"Accept: */*",
"Cache-Control: no-cache",
"Connection: keep-alive",
"Host: afisha.yandex.ru",
"accept-encoding: gzip, deflate",
"cache-control: no-cache"
),
));
$response = curl_exec($curl);
$err = curl_error($curl);
curl_close($curl);
if ($err) {
echo "cURL Error #:" . $err;
} else {
echo $response;
}