∵∠BAC=90°，∠B=60°，∴∠ACB=90°-60°=30°，∵△AB′C由△ABC绕点A顺时针旋转90°得到，∴AC′=AC，∠C′AB′=∠CAB=90°，∠AC′B′=30°，∴△ACC′为等腰直角三角形，∴∠AC′C=45°，∴∠CC′B′=∠AC′C-∠AC′B′=45°-30°=15°．故答案为15°．
