No, I'm pretty sure you can't. On xbox.com if I search for it it doesn't say anything about buying it like it does for Halo: Combat Evolved, which says you can buy it for 1200 Microsoft points (About £9-£10).
If you have it for your Xbox Original it will play in a new xbox 360 just fine. If you don't you can buy it for just under £15 on amazon, or about £5 used.
Xbox Original games do not have achievements and don't show up on your played games, but they do work fine on your 360 - they save and load and all that
Did this solve your problem?
Sorry this didn't help.
Great! Thanks for marking this as the answer.
How satisfied are you with this reply?
Thanks for your feedback, it helps us improve the site.