Probably obtained its name from Andrew Rankine, an energetic burgess, who built a remarkable house in the Vault called “Andrew Rankine’s Tower” in 1607. The building was demolished when the old Town House was extended in 1868. He was a shipowner in Dundee, and his name frequently appears in the Shipping Lists of the period. Apparently his residence was here previous to 1607, and the name has persisted till the present day. The most notable fact in connection with Rankine’s Court is that within a mansion in this Court the famous George Dempster of Dunnichen was born in 1732, and spent his early years here.
In 1677 the first George Dempster was born at Monifieth, and settled early in Dundee, where he became a leading merchant and banker, and lived in Rankine’s Court, acquiring the estates of Dunnichen, Newbigging, Conachie, Laws, and Ethiebeaton, all in Forfarshire. He made the most of his fortune as an exporter of grain, and was so blamed by the inhabitants for this traffic during a time of famine, that in 1720 his house in Rankine’s Court was raided by the mob and many valuables were carried away. His son John carried on the business, and George, the eldest son of John, was born in the Dempster mansion house. For many years George Dempster was Member of Parliament for Dundee, and his name is familiar to this day as a practical philanthropist. He died in 1818, respected by all classes of the community. An extension of Messrs. Keiller’s confectionary Works in 1887 absorbed some of the buildings in Rankine’s Court and the adjoining Gray’s Close, the latter of which had been in existence for over four hundred years.
Source: ‘Glimpses of Old and New Dundee’ – A.H. Millar, January 1925