To add a like to a photo you need to do it via POST. The following is an modified version of your code to do this.
<?php
$url = "https://api.instagram.com/v1/media/615839918291043487_528338984/likes";
$fields = array(
'access_token' => '191573449.9e262d9.ff708911edcd4f809ca31dd76d08c0ba'
);
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_POST, true);
curl_setopt($ch, CURLOPT_POSTFIELDS, http_build_query($fields));
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$response = curl_exec($ch);
curl_close($ch);
echo $response;
?>