Richard Rawlinson was born in 1690, the third surviving son of a prosperous family of vintners. His father, who had been knighted by James II, was to become Lord Mayor of London in 1705–6. Richard, like his eldest brother, Thomas, was educated at St Paul's, Eton and St John's College, Oxford. The two brothers were similar in many ways. Both had Jacobite leanings, were Tory in their political affiliations and shared an interest in past history. Conscious of the widespread damage to ecclesiastical artefacts and historical records caused by the dissolution of the monasteries and by the Civil War, both were concerned to rescue and preserve as much as was possible for posterity. It thus followed that from an early age they became avid collectors of historical material both antiquarian and contemporary. However, in character the two appear to have been very different. Thomas was a hedonist and a lavish spender with little thought for the consequences. Richard was serious, careful, and from an early age showed a strong sense of responsibility.

At university Richard's interest in antiquarian studies developed rapidly, influenced firstly by his admiration for Anthony Wood, a biography of whom he published while still an undergraduate, and secondly by his lasting friendship with Thomas Hearne, who at that time was Underkeeper at the Bodleian Library. Hearne records that Rawlinson's rooms at St John's resembled a veritable museum, containing among much else civil and ecclesiastical charters, a rare breviary on vellum, a manuscript account of the funeral of the Earl of Essex, a transcript of the deathbed prayers of James I, Saxon and Roman coins, and an inscribed stone from the convent of Godstow. The collecting of epitaphs from all over the country was a favourite occupation of both brothers.

However, this pleasant existence was soon to be threatened by family problems. Sir Thomas Rawlinson had died in 1708, the year of Richard's matriculation. His expenses were initially met by his mother as trustee, but when she remarried in 1711 he felt his financial situation sufficiently at risk to take legal action, although the outcome is unknown because his new stepfather died suddenly after only a year of marriage.