The party claimed the move would also reduce the chances of young people who find themselves in jail reoffending, which currently stands at 34%.
It comes after figures last year revealed that 80% of prisoners are functionally illiterate, making employment opportunities hard to come by upon release.
Tory justice spokeswoman Margaret Mitchell has urged the Scottish Government to introduce mandatory testing for reading, writing and mathematics for young people who receive custodial sentences.
She said their time in detention could be spent improving their skills and enhancing their ability to pursue work or training.
Ms Mitchell said: "As it stands, young offenders can spend years in and out of prison without being offered anything in the way of support.
"If prisoners are being released with no literacy or numeracy skills, there is no doubt it will increase the chances of them returning to prison in the future.
"If the SNP government is genuinely serious about reducing reoffending, it has to address these worrying literacy and numeracy statistics for offenders."