Ms Ginsburg, speaking in a wide-ranging conversation with the BBC's Razia Iqbal, also implied that senators who have already expressed their verdict in the president's likely impeachment trial should be disqualified.
She said: "Should a trial be impartial? Of course. That's the job of a judge to be impartial."
Ms Igbal asked: "So if a senator says, 'I've already made up my mind and the trial doesn't exist at the moment,' there is no accountability, is there?"
Ms Ginsburg replied: "If a judge said that, a judge would be disqualified from the case."
She also invoked a statement from former Justice William Rehnquist, saying: "The day a judge stops being impartial, and starts to do things to please the home crowd, that's the day the judge should step down from office."
On Twitter, the president suggested that the Supreme Court could intervene, saying: "Radical Left has NO CASE. Read the Transcripts. Shouldn't even be allowed. Can we go to Supreme Court to stop?"
Ms Ginsburg said: "The truth is, the judiciary is a reactive institution. We don't have a program, we don't have an agenda. We react to what's out there."
Ms Iqbal's conversation followed accusations of collusion between the president and Republican senators, ostensibly acting as the impartial jury in a senate trial that's likely to follow the House's upcoming vote supporting the president's impeachment.
Last week, Senate Majority Leader Mitch McConnell told Fox News that he is in "total coordination" with the White House as the Senate prepares for a trial, in which he said there would be "zero chance" the president would be removed from office.
He said: "Everything I do during this, I'm coordinating with the White House counsel. There will be no difference between the president's position and our position as to how to handle this."
At the White House on Friday, Mr Trump, asked whether he would whether a longer or shorter trial, said: "I'll do whatever I want."
On Tuesday, Mr McConnell responded to Senate Minority Leader Chuck Schumer's request for Trump appointees to appear as witnesses in the trial, after the White House failed to call witnesses, introduce evidence and send counsel to House hearings.
Mr Schumer said: "Impeachment trials, like most trials, have witnesses. To have none would be an aberration ... what are they afraid the witnesses are going to say?"
Mr McConnell had accused Mr Schumer's request as an attempt to "short circuit" the trial process.
On Monday, the 86-year-old Supreme Court justice was awarded the $1m Berggruen Prize for Philosophy and Culture, which she said she will distribute to several nonprofit organisations.
She recently agreed to put a temporary freeze on the release of the president's records from Capital One and Deutsche Bank while Mr Trump appeals a federal court ruling that said those records can be released under a Congressional subpoena.
The Supreme Court will hear opening arguments for several separate cases related to the presidents' financial records in March.
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