The singer performed a reworked version of her hit 'You And I' to mark the start of Obama's second term in office at a private show for his staff.
"You won twice," GaGa congratulated the audience, who responded by cheering loudly.
GaGa wore a long white dressed, customised with bubble ball shoulder pads, while playing the piano through the set.
The star also performed her hit 'Born This Way' and was joined on stage by jazz legend Tony Bennett.
Meanwhile, producer Zedd has revealed that GaGa still has a lot of work to complete on her third studio album ARTPOP, despite an expected release date of spring 2013.