The US wants TikTok sold or banned because of alleged links between ByteDance and the Chinese state, links that both TikTok and ByteDance have always denied.
The bill introducing the law said it was intended to “protect the national security of the United States from the threat posed by foreign adversary controlled applications”.
Trump opposes the ban – despite supporting one during his first term – partly on the grounds that it could help Facebook, which he has accused of aiding his 2020 election loss.
Trump’s second term, however, won’t begin until he is inaugurated on 20 January, the day after the deadline set out in the law.
In its filing to the Supreme Court, submitted on Monday, TikTok asked for a “modest delay” to the enforcement of the ban to “create breathing room” for a review by the Court and to allow the incoming administration to “evaluate this matter”.
It described TikTok as “one of the most significant speech platforms” in the US and said the ban would do “immediate irreparable harm” to the company and its users.
Earlier this month, the company’s bid to have the ban overturned was rejected by the federal appeals court, which found that the law was the “culmination of extensive, bipartisan action by the Congress and by successive presidents”.