A total of 44,826 units were sold, an increase of just over 2.5% on the same period last year.
The UK as a whole saw the number of cars sold rise by 6% to 492,774, according to the Society of Motor Manufacturers and Traders.
March is typically a strong month for car registrations, as it is when new number plates are released.
Scottish Motor Trade Association chief executive Douglas Robertson said: "We are very pleased to see another record month for Scottish new car registrations.
"Though the increase is small, it is close to what we expected.
"Whilst fleet and business sales have increased over the last 12 months, the Scottish market remains consumer-driven and we have little doubt that the availability of PCPs and other finance options continues to drive the market."
Top Scottish sellers in March
1. Vauxhall Corsa  3,095
2 Ford Fiesta   2,471
3. Ford Focus 1,294
5. Renault Clio 1,240
5. Vauxhall Mokka 1,179
Source: SMMT
The biggest-selling car last month was the Vauxhall Corsa, followed by the Ford Fiesta and Ford Focus.
Commenting on the figures, Euan Murray of Barclays Corporate Banking said: "The UK and Scottish motor trade's winning streak continued last month in record style, with new car sales lifted by March's all-important plate change and strong demand for fleet vehicles.
"The question on everyone's mind is how long this phenomenal run can continue and whether April will be able to drive home another record month."
Scotland's motor trade has reported another record month for new car registrations.