The sparrowhawk, which had been killed with a pellet gun, was dumped in a drainage ditch inside a plastic bag in Thorne, near Doncaster.
It was discovered by a member of the public close to the canal on 10 April 2022.
PC Sarah Barrowcliffe, of South Yorkshire Police, said: “This was a shocking act of violence against a beautiful and defenceless bird.”
South Yorkshire Police has appealed for information about the shooting.