"Armaja Das" by Joe Haldeman. I found a mention of it in Joe Haldeman by Joan Gordon.
"Armaja Das" is no more cheery - here destiny is in the form of a gypsy curse that cannot be avoided, even by the unbeliever. It sets up a chain reaction that turns civilization to rubble. "Armaja Das" was written to order and, after some research on gypsy lore, "it was child's play to toss together gypsy curses, computer science, and minority assimilation into an 'ancient horror in modern guise' " (introduction to "Armaja Das," ID). The atmosphere is quite disturbing for a piece of child's play: the empathetic computer that dies to save a man and the carnage its kindness causes make the story more haunting than its seemingly casual birth would suggest.
This page mentions the nuclear war aspect, "A Gypsy curse, transferred to a computer imbued with empathy circuits, indirectly brings on the nuclear end of the world." I have also confirmed the same doing a Google Translate on a copy of the story I found posted online in Spanish.
Podrían repararse partiendo de cero; se les podría borrar todo el programa y reprogramarlos después. Pero no se haría nunca porque quedaban dos ordenadores muy grandes y especializados que no tenían circuitos de empatía y por lo tanto eran inmunes. No podían tener circuitos de empatía porque su trabajo era el asesinato, el asesinato nuclear. Uno estaba debajo de una montaña en Colorado Springs y el otro debajo de una montaña cerca de Sverdlosk. Ambos podían resistir el impacto directo de una bomba atómica. Los dos evaluaban constantemente la situación del mundo en términos reales y los dos tenían la única función de decidir cuándo el enemigo estaría lo suficientemente debilitado como para hacer probable la victoria tras una contienda nuclear. Cada uno vio cómo la civilización enemiga detenía su marcha repentinamente.
Dos bandadas de proyectiles atómicos cruzaron sus estelas por encima del Pacífico Norte.
Here it is in the original English:
They could be rebuilt from the ground up; erased and then reprogrammed. But it would never be done. Because there were two very large computers left, specialized ones that had no empathy circuits and so were immune. They couldn’t have empathy circuits because their work was bloody murder, nuclear murder. One was under a mountain in Colorado Springs and the other was under a mountain near Sverdlosk. Either could survive a direct hit by an atomic bomb. Both of them constantly evaluated the world situation, in real time, and they both had the single function of deciding when the enemy was weak enough to make a nuclear victory probable. Each saw the enemy’s civilization grind to a sudden halt.
Two flocks of warheads crossed paths over the North Pacific.
It was a few search results down for short story computer "gypsy curse"
