My guess would be "Chain of Fools," he belted out a few bars in Detroit a few months back--Check it out!
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As fun as some of the other answers are, I would prefer to think she'd sing something more dignified like James Weldon Johnson's "Life Every Voice And Sing" (aka Black National Anthem).

YouTube took down the Aretha Franklin version of Lift Every Voice, but there is a version by the Great American soprano Leontyne Price.  Price starts singing the song at about 3:30 into the video clip.  Ms. Price talks about the White House, an Abraham Lincoln portrait (that hangs in the WH), and performing fo US Presidents.

Life Every Voice & Sing (1st Verse):

Lift every voice and sing, 
'Til earth and heaven ring, 
Ring with the harmonies of Liberty; 
Let our rejoicing rise 
High as the listening skies, 
Let it resound loud as the rolling sea.  
Sing a song full of the faith that the dark past has taught us, 
Sing a song full of the hope that the present has brought us; 
Facing the rising sun of our new day begun, 
Let us march on 'til victory is won.

Or, Aretha might sing a standard like Amazing Grace,  Nessun Dorma or something..
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