You are not legally required to provide your social security number on college applications: your social security number is private. Schools are not required to ask for it. It will be required for a college loan, but it should not be required for a college application. That’s why I recommend that you do NOT put a social security number on your transcript.
I can teach you how to create transcripts and records that win scholarships. Click to download samples of what we used to do it ourselves. The HomeScholar Record Keeping Samples
For more information, read this document from the Social Security Administration: Legal requirements to provide your Social Security Number.