The man was spotted by Metropolitan Police officers after 1pm on Sunday and "quickly challenged".
He was subsequently arrested on suspicion of trespass and for possession of Class-A drugs, according to Sky News.
The man was then passed into the custody of Thames Valley Police. The police said he has since been bailed, and an investigation is ongoing.
Sky News understands no members of the Royal Family were in the castle at the time.
The police added that the man had not entered the inner grounds of the castle.
It is a criminal offence to trespass on a protected site designated under the Serious Organized Crime and Police Act 2005.
MA/PR
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