The party are also backing calls from Keir Bloomer – a top education expert - to reduce bureaucracy in schools and make it easier to enter the profession of teaching.
In today’s Courier, the architect behind the SNP's own Curriculum for Excellence said it was a serious error to leave international education rankings – a benchmark for how schools are performing.
He also said a "grossly overregulated" education system was turning teachers away from the profession.
The Scottish Conservatives are putting pressure on the Scottish Government to commit to re-entering Scotland into all the main international education comparison tests in their manifesto.
The party have also made empowering school leaders one of their top priorities if they were to become the official opposition to the SNP at Holyrood.
Scottish Conservative young people spokeswoman Liz Smith said:
"Keir Bloomer is one of Scotland's foremost educationalists. He speaks with authority and his views are always backed up by good quality evidence and careful consideration of the facts rather than political rhetoric.
"He is therefore someone to whom we should pay attention not least because of his experience in local government and several educational think tanks.
"He is absolutely right when he tells the First Minister that she should re-instate Scotland in the TIMMS and PIRLS measurements and to reduce the amount of regulation and bureaucracy within education, much of which is stifling new initiatives and preventing headteachers from enjoying greater autonomy."