Bose-Einstein correlations in pairs of charged kaons produced in a sample of 3.9 million hadronic Z0 decays have been measured with the OPAL experiment at LEP. Charged kaons were identified in the central tracking detector using their specific energy loss in the drift chamber gas. The correlation function was studied in two-jet events using a double ratio, formed by the number of like-sign pairs normalised by a reference sample in the data, divided by the same ratio in a Monte Carlo simulation. The enhancement at small values of the four-momentum difference of the pair was parametrised using a Gaussian function. The parameters of the Bose-Einstein correlations were measured to be λ=0.82±0.22+0.17−0.12 for the strength and R0=0.56±0.08+0.08−0.06 fm for the kaon source radius, where the first errors are statistical and the second systematic. Corrections for final-state interactions are discussed.