Ms Orr, who died last October from breast cancer, wrote an account of two separate attacks in her memoir Motherwell: A Girlhood, which has been published posthumously.
The writer said she was left "terrified of men" following the sexual assaults at the university, where she studied English literature.
"They giggled hysterically but quietly throughout. I made no sound," she wrote.
Orr, who was born in Motherwell, was made the first female editor of The Guardian's Weekend magazine in 1993.
She was married to writer and critic Will Self for 11 years.