The Markit Report on Jobs: Scotland, which surveys around 100 recruitment and employment consultants across the country, found temporary placements are also growing.
The rate of increase in permanent staff in Scotland in March was faster than the UK-wide average but growth in temporary positions was slower than the across the UK as a whole.
The report found one reason behind the growth was a strengthening in demand for staff among Scottish businesses.
March had the sharpest growth in demand for permanent staff of the past six months and the jump in temporary openings was the highest since December 2014.
Areas which had the strongest growth in demand were nursing, medicine, care, IT, hotels and catering.
However, demand fell for executive, professional and blue collar workers.
Pay for both permanent and temporary workers rose in March but at a slower rate than the previous month.
The survey pointed to a tightening of the Scottish labour market, with a decrease in candidate numbers.
Markit economist Phil Smith said: “Recruiters reported another rise in the number of people placed in jobs in March, rounding off a better quarter for the industry than the final three months of 2015.
“However, there remained the issue of a lack of available candidates, which showed a sharper decline and kept pressure on businesses to offer higher starting pay.
“Demand for staff continued to strengthen across most job types in March, the exceptions being the fields of executive, professional and blue-collar work where the survey found falling numbers of vacancies.”