The site began linking to the president’s page on Monday after his Democrat rival Joe Biden was announced as president-elect at the weekend.
The loser.com domain name has reportedly been registered to comedian Brian Connelly since the early 1990s.
He has used the website to target other celebrities and politicians over the years, including former US president Barack Obama, 2000 presidential candidate Al Gore, who lost to George Bush, and American rapper Kayne West.
Mr Trump is still insisting he has won the 2020 presidential race, despite Mr Biden securing 290 electoral college votes – 20 more than the 270 needed to win – as well as the popular vote.
Over the weekend, eagle-eyed Twitter users spotted that searching the term “loser” on the social media site delivered Mr Trump’s account as the top result.
Twitter said its search results are not selected or curated by members of staff and that it came down to an algorithm which gives results based on certain terms being frequently associated with an account.
“If an account is mentioned often alongside certain terms, they can become algorithmically surfaced together as an association,” Twitter said in a statement.
“These associations are temporal and ever changing based on how people tweet.”
Mr Trump has been known to call his opponents “losers” – and even faced a backlash over reports alleging he mocked American soldiers killed in action as “losers”.
A report in The Atlantic claimed he was unwilling to honour the US’s war dead, instead repeatedly calling lost service members and prisoners of war “losers” and “suckers”.
Mr Trump vehemently denied the reports.
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