The bird was discovered on a doorstep on Saturday, September 15.
It was found outside an address on Cross Street, Scarborough.
RSPCA inspector Laura Barber said: “This poor pigeon was just sitting there with the crossbow arrow all the way through their little body. It’s shocking that someone would do something so cruel, deliberately causing so much suffering.
“Sadly there was no other option but to put the bird straight to sleep.”
Another arrow was found without its tip nearby.
“I am very concerned that someone is using a crossbow in the area, and clearly, on at least one occasion, have targeted wildlife,” said Inspector Barber. “The police have also been notified,” she added.
Anyone who saw anything or has any information about what happened is urged to contact the RSPCA inspector appeal line on 0300 123 8018 and ask to leave a message for Inspector Barber.
To help the RSPCA continue investigating incidents like this please visit: www.rspca.org.uk/give