The current edition of the AMA manual does not specifically reference using URL shorteners, but previously the AMA style blog (AMA Style Insider) has stated that the use of shortened URLs for scientific publications is not encouraged. An assignment or thesis usually follows the same expectations as a published paper, but you can negotiate with your lecturer if they will accept shortened URLs if the work is not actually intended for publication.

"Using bit.ly to shorten URLs in the reference list for a scientific article is probably not consistent with best practices. We do use bit.ly in our style manual tweets, to save space, but the reference list of a scientific article is a different matter. Use of the full URL allows readers to know the original domain name (like nih.gov). We are also not sure how permanently stable a shortened link would be."  https://amastyleinsider.com/2012/12/18/questions-from-users-of-the-manual-18/