Graci is a distinctive girls' name in United States, ranking #1606 in 2003 with 120 recorded births. The name reached its all-time peak in 2004 with 130 births ranking #1536. Since 1996, the popularity has increased by 1,614.3%. In 2003, approximately 1 in every 15,225 girls born was named Graci. FALLING Recent data shows the name is currently falling.