The rise of machine learning technology inspires a boom of its applications in electronic design automation (EDA) and helps improve the degree of automation in chip designs. However, manually crafted machine learning models require extensive human expertise and tremendous engineering efforts. In this work, we leverage neural architecture search (NAS) to automatically develop high-quality neural architectures for routability prediction, which guides cell placement toward routable solutions. Experimental results demonstrate that the automatically generated neural architectures clearly outperform the manual solutions. Compared to the average case of manually designed models, NAS-generated models achieve $5.6\%$ higher Kendall's $\tau$ in predicting the number of nets with DRC violations and $1.95\%$ larger area under ROC curve (ROC-AUC) in DRC hotspots detection.