With 1.06 × 108 ψ(3686) events collected with the BESIII detector, the branching fraction of ψ (3686) → ωK+K- is measured to be (1.54 ± 0.04 ± 0.11) × 10-4. This is the most precise result to date, due to the largest ψ(3686) sample, improved signal reconstruction efficiency, good simulation of the detector performance, and a more accurate knowledge of the continuum contribution. Using the branching fraction of J/ψ → ωK+K-, the ratio β(ψ(3868) → ωK+K-)/β(J/ψ → ωK+K-) is determined to be (18.4 ± 3.7)%. This constitutes a significantly improved test of the 12% rule, with the uncertainty now dominated by the J/ψ branching fraction.