The rate has dropped this low three times: between February and April and January and March this year, as well as between January and March 2019.
The rate is lower than that of the rest of the UK (3.8%).
It was unchanged from the previous quarter, increasing by just 2,000, but decreased by 1.1 percentage points when compared with the same quarter last year.
Similarly, employment increased by 1.2 percentage points during the same period, with 73,000 more people in work.
The statistical body reported 75.4% employment between April and June, with around 2.7 million people working, a drop of 0.1 percentage points, equivalent to 25,000 people.
But despite the relatively positive news for Scotland, estimated wage growth has fallen behind that of the rest of the UK.
Median monthly income for payrolled employees in July was £2,118, an increase of 5.3% on the same period in the previous year, but behind the 6.6% rise seen in the UK.
Estimated wages, the ONS said, rose in Scotland by 12.8% between February 2020 – the last month before the start of the pandemic – and the most recent month, compared with 13.4% in the UK as a whole.
Employment Minister Richard Lochhead said: “The Scottish economy and labour market are continuing to show resilience, although the employment rate has decreased slightly over the quarter, the unemployment rate was a joint record low in the Scottish series.
“Additionally, the employment rate for women in Scotland was the highest since the labour force survey estimates were first published in 1992.
“This is despite the serious challenges Scotland is facing as we recover from the pandemic, with the cost-of-living crisis, the continued impact of Brexit and the economic consequences of Russia’s illegal invasion of Ukraine all impacting on the economy.