A kestrel was hit with a baseball bat in the Bradley Park area of Huddersfield on Friday.
The West Yorkshire Police Wildlife and Rural Crime Unit were called to the scene and are searching for the suspect.
The kestrel is included on the Amber List of Birds of Conservation Concern due to the moderate decline of the UK breeding population, according to the RSPB.
Officers want to speak to anyone who may have witnessed the attack.
If you have information on the incident call police on 101 quoting reference number 13200421413.