The offences are alleged to have taken place between November 2022 and May 2024, Thames Valley Police said.
Mr Spencer-Churchill, the former Marquess of Blandford, was arrested on 13 May 2024.
The twice-married aristocrat inherited his dukedom in 2014, following the death of his father, the 11th Duke of Marlborough.
He is a first cousin, three times removed, of Sir Winston Churchill and a distant relative to the late Princess Diana through the Spencer family.
His ancestral family home is Blenheim Palace in Woodstock – Sir Winston’s birthplace.
However, he does not own or run the Unesco World Heritage Site.
The duke’s representatives have been approached for comment.
