This boat carrying refugees had a broken engine, Indonesian officials say
This is the second boat carrying Rohingyas to have arrived in Aceh in the past two days.
Another boat with 180 on board is thought to have sunk in early December, NGOs and family members say.
The Rohingya are a persecuted ethnic minority in their home in Myanmar.
More than a million now live in overcrowded camps in southern Bangladesh following a campaign against them by the Myanmar military which the UN believes could amount to a genocide.
The wooden fishing boat, crammed with Rohingya men, women and children, set sail from southern Bangladesh on 25 November.
Six days later, the engine broke down, and the boat began to drift westward from Malaysian waters to the seas off the northern tip of Indonesia, and then into Indian waters south of the Nicobar islands.
Activists and family members were able to make occasional phone calls to the boat, and, together with the UN Refugee Agency, appealed to the Indian and Indonesian authorities to help. People on board said they were starving and that many had died.
However, the Indian navy appears only to have given them some food and water and towed them back to Indonesia, where they drifted offshore for six more days until they were finally allowed to land, some 1,200 miles (1,900km) from where they had first set off.
On Sunday, a wooden boat with at least 57 men on board drifted on to a beach in Aceh with a broken engine, local officials say.
They were described as hungry and weak after spending a month at sea. At least three men were taken to hospital.
"The boat had a broken engine and it was carried by the wind to a shore in Ladong Village in Aceh Besar [district]," the spokesman said. "They said they have been drifting at sea for a month."
A local immigration official told AFP the refugees would be temporarily placed at a government facility.
Meanwhile, the UN refugee agency fears 180 refugees on board another boat have probably died. Spokesman Babar Baloch said relatives had been told there were signs the boat was cracking: "We're talking about desperate people - Rohingya refugees and full families, parents with their children."
The International Organisation for Migration said it had been raising the alarm for some time about boats heading for Malaysia and Indonesia carrying refugees who had not had food or water for weeks.
Hundreds of thousands of Rohingyas still live in Myanmar, formerly known as Burma, but are subjected to apartheid-like restrictions and discrimination.
In recent months, they have been trying to escape from overcrowded refugee camps in southern Bangladesh by taking high-risk sea journeys at this time of year, after the monsoon in the region has passed, to try and reach Malaysia, where there is a large Rohingya community.
Their numbers have grown because of deteriorating conditions in the camps, while more Rohingya who are still in Myanmar are also trying to leave following the military coup there last year.
At least five boats are known to have left in the past two months.
-- Courtesy of BBC News