Her Late Majesty The Queen at the university in 2005
Annie Lawlor, 23, studying law, said: "It’s a bit old-fashioned to have it played at a ceremony supposed to be celebrating the achievements of the individual student."
The move has been criticised by some, branding it "contemptuous".
Free Speech Union director Toby Young said: "Why are Britain's most prestigious universities openly contemptuous of the country's history and heritage?".
A University of Bristol spokesperson said: “The University routinely updates aspects of its Graduation ceremonies, which included the 2020 decision that the National Anthem would be played when representatives of the Royal Family, such as the Lord-Lieutenant, are in attendance."
In November, the university announced it would distance itself further from slave trader Edward Colston following a public consultation.
Seven buildings at the university named after families, including Wills and Frys, with links to slavery should be renamed according to protesters.
Vice-chancellor and president of the university, Professor Evelyn Welch announced the decision to strip Colston's emblem from the University's logo.
In an open letter, she also apologised to those who had experienced racism at the institution.