I believe the most common translation is 共感.
I'm Japanese, but I've never heard 共情. I looked up the word in several J-J dictionaries, but it's not in 広辞苑, 大辞林, 大辞泉, 新辞林, 新明解国語辞典, 明鏡国語辞典, etc.. Google search results suggest that 共情 is a relatively-new Chinese translation of "empathy".