If you registered for your ACT through ACT, Inc. using online registration, then you should be able to use your old login to access your ACT account and find your old scores. If you run into problems, then contact the ACT, Inc. directly and inquire about alternative methods: http://www.actstudent.org/faq/contact.html

If going through the ACT company doesn't work, then try your high school for old records or your college. Either of those places may still have your scores.