Okoumou, an immigrant from the Democratic Republic of Congo, pleaded not guilty in federal court to charges of trespassing, disorderly conduct and interfering with agency functions, according to Fox News.
Okoumou is an active member of New York-based activist group Rise and Resist, whose members had previously held an "Abolish I.C.E" banner at the statue.
The climber ascended from the observation point, National Park Service spokesman Jerry Willis said. In a democracy, we do not put children in cages. "She could do some damage".
Okoumou, 44, of Staten Island, was expected to appear in federal court in Manhattan later Thursday.
Jay Walker, an organizer with Rise and Resist which opposes the Trump administration's policies, aaid the other demonstrators had no idea Okoumou would make the ascent, which wasn't part of the planned protest. "Trump has wrecked this country apart".
"She's been taken into custody amicably, peacefully, without any injuries, or injuries to our officers, thank God".
She was arrested in August previous year for trespassing, obstruction of government administration and misdemeanour assault during a demonstration against the state Department of Labor on Varick Street, news site Daily News reports.
The climber has been there for about three hours, with police talking to her.
The incident forced park officials to evacuate the island on July 4 - one of the most popular days of the year for visitors.
Lt. Michael McGuiness, also from Long Island, says multiple NYPD units assisted in the successful rescue.
Demonstrations have recently taken place across the U.S. after it emerged that Ice agents had separated thousands of young children from parents who had entered the United States illegally. Each count carries has a maximum penalty of six months in prison and a fine.
"Patricia was trying to convey the words that are on the statue-'Bring us your exhausted, your poor, '" demonstrator Martin Quinn said, paraphrasing.