Here's a place to start. Some of these articles have measures attached. Also, it depends what kind of empathy you're talking about. I hope this helps!
Henry, B. C. (2006). Empathy, home environment, and attitudes toward animals in relation to animal abuse. Anthrozoos, 19(1), 17–34. https://doi.org/10.2752/089279306785593847
Daly, B., & Morton, L. L. (2006). An investigation of human-animal interactions and empathy as related to pet preference, ownership, attachment, and attitudes in children. Anthrozoos, 19(2), 113–127.
Paul, E. S. (2000). Empathy with animals and with humans: Are they linked? Anthrozoos, 13(4), 194–202. https://doi.org/10.2752/089279300786999699
Taylor, N., & Signal, T. D. (2005). Empathy and attitudes to animals. Anthrozoos, 18(1), 18–27.