Mrs Clinton gave the graduation address at a ceremony to mark the 600th anniversary of the founding of St Andrews University.
Mrs Clinton told an audience of education leaders, university staff and students: "We need more voices speaking up for universal human rights.
"We have honoured some of the great advocates here today who have spoken out courageously for women's rights, gay rights and religious understanding, showing us that our communities and institutions are strongest when equality and opportunity are open to all people and freedom of conscience is respected.
"Here in the home of the Scottish Enlightenment and the great contributions from Scottish universities, we need to be reminded that it paved the way for much of the progress we now take for granted, not only in the West but around the world."
Mrs Clinton was conferred with a doctor of laws degree in recognition of her achievements as a politician and diplomat.
She received the doctorate from the veteran Liberal Democrat politician and chancellor of St Andrews, Sir Menzies Campbell.
The award marked her efforts to champion the causes of education, human rights, democracy, civil society and promoting opportunities for women around the world, the university said.