The total, which includes people who are out of work and not eligible for benefits, increased 7000 over the quarter from June to August and is 10,000 more than it was at the same time last year.
That situation is in contrast with the UK as a whole, where unemployment fell 50,000 over the same period to 2.53million, the lowest since the spring.
The Scottish unemployment rate of 8.2% remains higher than the 7.9% rate for the UK.
It is the second month in a row unemployment in Scotland has increased, after a number of months when the total had been falling.
The figures also showed the number of people in work in Scotland from June-August dropped 1000 to 2.49m, although this was 16,000 higher than the same period last year.
Meanwhile the number of Scots who are out of work and claiming Jobseeker's Allowance fell 1300 from August, to stand at 139,900 in September.
Scottish Secretary Michael Moore said the country's rising unemployment level was "cause for concern".
But he said there were some "positive signs", highlighting the third consecutive fall in the numbers of people claiming Jobseeker's Allowance.
Mr Moore said: "Unemployment has a major impact on families and communities and our priority is to create opportunities to help people back into work.
"These are difficult economic times in the face of a world economy facing a number of challenges."
"We will continue to do as much as we can to help people find work through targeted support available at Scotland's JobCentre Plus network."