curl \
-F "file=@translation-memory.tmx" \
http://api.crowdin.net/api/project/{project-identifier}/upload-tm?key={project-key}

<?php
  $post_params = array();
  $request_url = 'http://api.crowdin.net/api/project/{project-identifier}/upload-tm?key={project-key}';
  $post_params['file'] = '@/home/crowdin/test.tmx';

  $ch = curl_init();
  curl_setopt($ch, CURLOPT_URL, $request_url);
  curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
  curl_setopt($ch, CURLOPT_POST, true);
  curl_setopt($ch, CURLOPT_POSTFIELDS, $post_params);

  $result = curl_exec($ch);
  curl_close($ch);

  echo $result;