Mrs Robinson, who was Irish president from 1990 to 1997, told the graduates they had been given a gift which "several thousand million people on this plant will never receive".
"You have been able to experience the unfolding of a new century, with all its opportunities and challenges, within an environment where the pursuit of knowledge was the ultimate aim," she said.
"Thanks to the guidance of your professors and to the exchange of views and experiences with your fellow students, you have been able to dig deeper and, hopefully, bring forth richer insights into the probing issues of our day.
"You have been given time and a space to examine your beliefs and to see the world in all its complexity, not just through your eyes, but also through the eyes of others.
"You have had the opportunity to develop that moral compass which can guide you through your life and help you to stick to your principles."
Mrs Robinson, presented with a Doctor of Laws by Glasgow Caledonian University, urged students to "think about the difference you could make and how you will define your community".
"It can be as simple as small acts of kindness to an elderly housebound neighbour, or support for the homeless or a local youth club," she said.
"As honorary president of Oxfam I would encourage some of you to be active in advocating fair trade and buying fair trade products, as well as campaigning against the spread of small arms the real weapons of mass destruction in our world today.
"Just remember, there is no limit to what you can do, and every individual can make a difference."
The 60-year-old imparted that message after being recognised for her "unequalled contribution in the fields of human rights and politics both at home and abroad".
She picked up her scroll in a ceremony at Glasgow Royal Concert Hall.
Conferring the degree, Maria Stafford, chairwoman of the University Court, hailed Mrs Robinson as "an extraordinary woman".
"In every generation there are a few people who stand head and shoulders above their peers and of whose achievements the average person can only stand in awe," she said.
"Mary Robinson is one such person. She is, by any standard, an extraordinary woman, intellectually, professionally, politically, and most particularly, in her pursuit of human rights and social justice.
"Her career has always been about making a difference. But what marks Mary out more specially is her ruthless pursuit of social justice and human rights, irrespective of gender, religion, race or colour."