In science, R is the symbol for the gas constant in the ideal gas law having a value of: [1]

$~ 8.314 \frac{J}{K \cdot mol} ~$

The first dominant use of R as a constant, as used in the various gas laws, seems to have been first used by French engineer Emile Clapyron in his 1834 Memoir on the Motive Power of Fire, where he states that Mariotte’s law (PV = k, at constant temperature) combined with that of Gay-Lussac's law (P = kT, at constant volume), the latter of which being derived by French chemist Joseph Gay-Lussac in 1802, gives the expression: [2]

$~ Pv = R(267 + t) ~$

This is sometimes referred to as the 'G-M law' or the 'law of Marriatte and Gay-Lussac'.

Etymology
The origin of the symbol R, prior to its 1834 use by Clapeyron, is difficult to pin down. This seems to be due to the fact often early versions of the gas laws were simply stated verbally.

The symbol could have been used in honor of Danish astronomer Ole Romer who in 1702 built the basic two-fixed point thermometer; a design later used by Daniel Fahrenheit in the construction of his thermometer. This, however, is a tentative guess?

In a 2003, American chemistry historian William Jensen, in his “The Universal Gas Constant R”, in which he attempts to "trace the history of the gas constant R and the probable reason for its representation by the letter R", suggested that R should be officially named after French chemist Henri Regnault. [3] On the surface this seems tenable, being that Regnault's circa 1847 experimental gas work was the basis of Irish physicist William Thomson's famous publication "An Account of Carnot's Theory of the Motive Power of Heat: with Numerical Results Deduced from Regnault’s Experiments on Steam”, the paper that stimulated German physicist Rudolf Clausius into founding thermodynamics. [3]

If one looks at the facts, however, this hypothesis falls apart. Specifically, at the time Clapyron was using R as a constant in his gas equations of 1834, Regnault was only twenty-four years of age at this point, being a recent graduate of the École Polytechnique two years prior, having only done work in organic chemistry at this point, and nothing in caloric gas theory. Regnault did not begin his work on the properties of gases and physics until the 1840s (nearly 15-years after the gas constant R was already in use); his key publication on this subject was in 1847 (and he only began to be cited by Clausius in 1850).

In fact, prior to the work of Sadi Carnot (1824), there were a number of more dominant investigators on the various gas laws: Alexis Petit (1818), Joseph Gay-Lussac (1800), Jacques Charles (1787), Daniel Bernoulli (1738), Edme Mariotte (1679), Henry Power (1661), Robert Boyle (1660), Robert Hooke (1657). In the "big history" sense of the matter, it would seem more appropriate to assume or possibly credit the symbol "R" to the "Roberts" (Boyle and Hooke) as they were the first to invent the pneumatical engine and to experiment with it to determine the first gas law, namely Boyle's law.

References
1. Daintith, John. (2005). Oxford Dictionary of Physics. Oxford University Press.
2. Clapeyron, Émile. (1834). “Memoir on the Motive Power of Heat”, Journal de l’Ecole Polytechnique. XIV, 153 (and Poggendorff's Annalender Physick, LIX, [1843] 446, 566).
3. (a) Jensen, William B. (2003). “The Universal Gas Constant R” (abstract: “this column traces the history of the gas constant R and the probable reason for its representation by the letter R.), J. Chem. Edu. 80: 731.
(b) William B. Jensen (faculty) – Department of Chemistry, University of Cincinnati.