Despite its importance, studying economic behavior across diverse, non-WEIRD (Western, Educated, Industrialized, Rich, and Democratic) populations presents significant challenges. We address this issue by introducing a novel methodology that uses Large Language Models (LLMs) to create synthetic cultural agents (SCAs) representing these populations. We subject these SCAs to classic behavioral experiments, including the dictator and ultimatum games. Our results demonstrate substantial cross-cultural variability in experimental behavior. Notably, for populations with available data, SCAs' behaviors qualitatively resemble those of real human subjects. For unstudied populations, our method can generate novel, testable hypotheses about economic behavior. By integrating AI into experimental economics, this approach offers an effective and ethical method to pilot experiments and refine protocols for hard-to-reach populations. Our study provides a new tool for cross-cultural economic studies and demonstrates how LLMs can help experimental behavioral research.