I think a very good approach to this is by putting your AI against different rating levels of the plain computer engine that chess.com has, and adjusting the rating of the computer and seeing how well your AI stands up to different ratings to get a good estimate of your AI's rating.
Coding a Chess AI
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I am aware that using a chess AI is strictly prohibited during a rated chess match, but I am programming a chess AI for a software engineering course in college and I would like to get a rating estimate of my AI for a presentation. I was wondering if there was a place where I can test my AI in order to get a rating, does anyone know?