Two boys were seen shooting the bird on the River Dearne near Middlewood Park, Darfield, at roughly 4pm on Sunday, June 27, South Yorkshire Police said.
The boys, who are thought to have been about 15 years old, ran off towards Doncaster Road.
A spokesperson from South Yorkshire Police, said: "Officers attended the scene and conducted a search for the boys, and attempted to locate the wounded swan to no gain.
"Enquiries are ongoing to locate those responsible."
Anyone who saw the incident is asked to contact police.
If you can help, please call 101 quoting incident number 651 of 27 June.
Alternatively, you can stay completely anonymous by contacting the independent charity Crimestoppers via their website here, or by calling their UK Contact Centre on 0800 555 111.
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