Over its 11-year history, the council has come in for criticism, including allegations that it has, at times, been co-opted by rights abusers who push resolutions attacking their geopolitical rivals, with genuine rights issues marginalized.
But the 47-member panel has had successes — thanks to support from Barack Obama's administration which held a seat on the council for most of his eight-year term, civil society groups say.
Many of the issues prioritised by Obama's UN envoys — including violations in North Korea, Myanmar, Sri Lanka and South Sudan — will remain on the agenda when the council opens its main annual session in Geneva on Monday.
Among the headline speakers are UN chief Antonio Guterres and Palestinian president Mahmud Abbas.
Trump's State Department has not yet named a replacement for Obama's envoy Keith Harper.
Veteran US foreign service officer Erin Barclay is scheduled to address the body on Wednesday.
Much of Trump's international agenda remains murky but rights advocates have warned that early signs are not good for either the council or the broader human rights agenda.
“Clearly 'America First' does not suggest an approach that (prioritizes) multilateral engagement,” said John Fisher of Human Rights Watch in Geneva, referring to Trump's starkly-defined foreign policy doctrine.
There is also “significant concern” about the US capacity to take a leadership role in the council based on Trump's early moves, he added.
“When the administration has issued an executive order that bans travel from seven mainly-Muslim countries it erodes the US's moral credibility and ability to engage in initiatives around the UN,” Fisher told AFP.
Trump's travel ban has been blocked in court.
Fisher also highlighted Trump's moves curbing rights for transgender people and his “stereotyping and scapegoating” of some migrants.
“I think one of the key challenges that the US will face is to demonstrate that it applies at home the same human rights and principles that it applies to others,” he said.
Last week, another spat blew up over freedom of the press after the White House barred several major US and international news organisations from a daily briefing and Trump denounced the media as the “enemy of the people”.
The move sparked outrage, with an editorial in the Los Angeles Times warning that Trump was demonstrating some “alarmingly authoritarian notions” in punishing organisations which ran stories critical of him.
The precursor to the rights council was the UN Commission on Human Rights, a body deemed so dysfunctional that former secretary general Kofi Annan scrapped it.
When the new council was born in 2006, the US administration of George W. Bush did not fight for a seat or meaningfully engage, according to a January report from the Council on Foreign Relations (CFR) think-tank.
The early years saw countries like Algeria, Pakistan and Saudi Arabia controlling the council, the CFR said, arguing that things began to turn when Obama's administration secured a seat in 2009.
The US began “to chip away at the council's deficiencies while strengthening its capacity as a credible international human rights
institution,” it said.
The think-tank's report agreed with Fisher that US influence on the council was decisive in setting up major probes in Burundi, North Korea, Syria and other hotspots.
The CFR urged Trump to take full advantage of the US council seat which expires in 2019.
Even if Trump's rights-related pronouncements have been “limited”, he has “stressed the need for the United States to be seen as winning on the international stage”, it said.
And engaging with the council could “advance these goals”, it argued.
For Fisher, next week will be a “litmus test” for Trump's administration.
He also argued that uncertainty about the US made this a moment for “other countries to strengthen their leadership”.