Successively universities were ranked based on peer reputation in the beginnings of 20th century, until 1983, the US news and World Report started ranking undergraduate universities which became an annual event from 1987 (Bastedo & Bowman, 2009). This was the first publication of university rankings
Many people say rankings began in the United States when the magazine U.S. News & World Report https://www.usnews.com published its first "America's Best Colleges" report in 1983. This ranking became and widely followed as updates were published.
In the U.K. The Complete University Guide first appeared in 2007.
Hazim Al Dilaimy Dear Dr. Hazim, I have answered the question in my recent published article Article Comparative Analysis of National University Ranking System i...
Rankings are a fairly new concept (when considering how long Universities have been around). Given that, as most responses would suggest rankings became common in the 20th century.