We report the first operation of a Ra⁺ optical clock, a promising high-performance clock candidate. The clock uses a single trapped ²²⁶Ra⁺ ion and operates on the 7s ²S_1/2 → 6d ²D_5/2 electric quadrupole transition. By self-referencing three pairs of symmetric Zeeman transitions, we demonstrate a frequency instability of 1.1 x 10^-13/√τ, where τ is the averaging time in seconds. The total systematic uncertainty is evaluated to be Δν/ν = 9 x 10^-16. Using the clock, we realize the first measurement of the ratio of the D_5/2 state to the S_1/2 state Landé g-factors: g_D/g_S = 0.5988053(11). A Ra⁺ optical clock could improve limits on the time variation of the fine structure constant in an optical frequency comparison. The ion also has several features that make it a suitable system for a transportable optical clock.