In your DirectAdmin panel go to 'cronjobs' section, I assume you already configured time interval for your cronjob, so you just need to adjust 'command' option, so try:
First option:
/usr/bin/php -f /home/your_user/public_html/your_script.php
This way you will call php script with php interpreter.
Second option:
lynx -source http://yourdomain.com/your_script.php
This way you will execute text based web browser lynx and open desired url so that php script can be run. Lynx is installed by default on most linux servers.
Also I believe that there is a option in DirecAdmin cronjobs section called 'Prevent email' check that so that you don't receive emails.