The human-centered word association test (WAT) serves as a cognitive proxy, revealing sociocultural variations through culturally shared semantic expectations and implicit linguistic patterns shaped by lived experiences. We extend this test into an LLM-adaptive, free-relation task to assess the alignment of large language models (LLMs) with cross-cultural cognition. To address culture preference, we propose CultureSteer, an innovative approach that moves beyond superficial cultural prompting by embedding cultural-specific semantic associations directly within the model's internal representation space. Experiments show that current LLMs exhibit significant bias toward Western (notably American) schemas at the word association level. In contrast, our model substantially improves cross-cultural alignment, capturing diverse semantic associations. Further validation on culture-sensitive downstream tasks confirms its efficacy in fostering cognitive alignment across cultures. This work contributes a novel methodological paradigm for enhancing cultural awareness in LLMs, advancing the development of more inclusive language technologies.