The most specific reference to the Declaration is made in the opening sentence, "Four score and seven years ago..." The year Lincoln refers to is 1776, when the thirteen colonies formally declared their independence from Britain. He then proceeds to say that the people who created the nation did so on the principle that "all men are created equal," a direct quote from the Declaration. More generally, Lincoln references the Declaration indirectly by characterizing the Civil War as a "new birth of freedom" (with the Declaration being the first birth of freedom.) Furthermore, Lincoln's references to government by the people echo some of the liberal rhetoric of the Declaration. The idea Lincoln wants to convey is that the struggle is about determining whether a government based on the will of the people can survive a civil war. It was, of course, the Declaration that first announced the principles of the new government to the world.
I agree with everything that is said in the previous answer. The references noted in that answer are the clearest references to the Declaration of Independence in the Gettysburg Address. I will simply add one other reference which is rather tangential and not as good as the ones in the first answer.
At the end of the address, Lincoln says that the men who have died at Gettysburg have died to ensure that
government of the people, by the people, for the people shall not perish from the earth.
This is, to some extent, a reference to the Declaration of Independence. The exact words that Lincoln uses are not in the Declaration, but the idea of democracy clearly is. When Lincoln talks about government of the people and by the people, he is talking about government that exists by the consent of the governed. This is part of the Declaration. When he says that government is for the people, he means that government is created in order to protect the rights of the people. This, too, is in the Declaration.
In this way, Lincoln's last line in the Gettysburg Address refers to the ideas in the Declaration of Independence, even if it does not use the exact words of the earlier document.