No. We should follow the Constitution. But we can learn from international law, absolutely. We can learn something this very day, as it happens, from the world's largest democracy. Too bad the Supreme Court didn't get it a few years back.
Perhaps evolving standards of respect for women, not to mention respect for the most minimal human decency, will bring about a change of heart.
P.S. When abolitionists tell us that we should adhere to the opinions of the "international community," what they actually mean is that we should adhere to the opinions of white people in Europe. The death penalty predominates among "people of color" (as the phrase goes) in the Orient, the Subcontinent, the Middle East, the Caribbean, most of Africa and most of North America.