C. Ethos
This is one of the three Aristotelian Rhetorical Appeals (Ethos, Logos and Pathos), which are language devices used by a speaker or author to persuade an audience into believing a certain point of view.
Ethos (or appeal to Ethics) specifically, is the appeal through the credibility or authority of a higher figure. In the case of this excerpt from the Declaration of Independence, God, in '...appealing to the Supreme Judge of the world for the rectitude of our intentions, do, in the Name...' - and also calls upon the 'Authority of the good People of these Colonies'.