Half of those surveyed said they has used ineffective methods, such as opening the window to try to beat tiredness.
The RSA published the findings as it and the gardaí launched their Easter safe driving appeal.
Two people died on Irish roads last Easter.
Gardaí say they hope no-one dies in road collisions this year and the force has appealed to people to be more careful.
Chief Superintendent Gabriel McIntyre said over a two-week period significant resources will be put in place to conduct checkpoint and enforce drink-driving legislation.
Noel Brett of the Road Safety Authority said driver fatigue is as dangerous as drink-driving.
He is advising people not to drive if tired and to think carefully before taking to the road in the days ahead.
