Thank you ! So if someone else needs this here is a working code to reboot a droplet via PHP using api v2 :

<?php
$data = array("type" => "reboot");
$data_string = json_encode($data);

$ch = curl_init('https://api.digitalocean.com/v2/droplets/DROPLET_ID/actions');
curl_setopt($ch, CURLOPT_CUSTOMREQUEST, "POST");
curl_setopt($ch, CURLOPT_POSTFIELDS, $data_string);
curl_setopt($ch, CURLOPT_HTTPHEADER, array(
    'Authorization: Bearer YOUR_TOKEN',
    'Content-Type: application/json',
    'Content-Length: ' . strlen($data_string))
);

$result = curl_exec($ch);
print_r($result);
?>

You would need to change YOURTOKEN and DROPLETID