The crime at the site of the 13th-century castle - which has Norman origins - took place overnight between May 19 and 20.
The castle, which was built to maintain order following the Harrying of the North, was not besieged during either the Civil War or the Wars of the Roses and is a relatively intact medieval survivor.
The graffiti was found on the main wooden entrance door.
A spokesperson for North Yorkshire Police said: “Pickering Castle is one of thousands of heritage sites that make our area such a great place to live and visit.
“We all need to work together to protect these sites, so that future generations can continue to enjoy them for many years to come. This can be achieved by increasing awareness of the heritage assets in our community, supporting rural watch schemes, and encouraging members of the public to report incidents around heritage sites.”
North Yorkshire Police regularly patrol heritage sites, and work with partner agencies to ensure they are protected. People who live and work near such sites - particularly in rural areas - are asked to help the police combat heritage crime:
Anyone with information that could assist the investigation into the damage at Pickering Castle should contact North Yorkshire Police on 101, select option 2, and ask for PC Louise Neville-Beck, or email [email protected]
Please quote the North Yorkshire Police reference number 12210121816 when passing information about this incident.