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A graphical regular representation of a group G is a Cayley graph of G whose full automorphism group is equal to the right regular permutation representation of G. In this paper, we prove that for Ree groups Ree (q) with q > 3, with probability tending to 1 as q → ∞ , a random involution y together with a fixed element x with order q – 1 gives rise to a cubic graphical regular representation of Ree (q) . A similar result involving a fixed element with order q + 3 q + 1 is also proved with the help of certain properties of Ree (q) given in [Leemans, D. Liebeck, M. W. (2017). Chiral polyhedra and finite simple groups. Bull. London Math. Soc. 49: 581–592]. [ABSTRACT FROM AUTHOR]