He was the son of Johannes Van Rensselaer (1708–1793), and Engeltie "Angelica" Livingston (1698–1746/47), descendants of ethnic Dutch and English colonists.

[4] His paternal 2x great-grandfather was the merchant Killian Van Rensselaer, one of the original founders of the Dutch colony, New Amsterdam.

One of their members had been found with a war wampum belt indicating alliance with the British against the colonists.

He cast his votes for the eventual 2nd President of the United States, John Adams, and Thomas Pinckney.

On April 23, 1765, Robert married Cornelia Rutsen (1747–1790),[11] the daughter of Colonel Jacob Rutsen and Alida Livingston on April 23, 1765, and had the following children:[12][3][13] Van Rensselaer died September 11, 1802, at the Van Rensselaer Lower Manor House.