We investigate global persistence properties for the non-equilibrium critical dynamics of the randomly diluted Ising model. The disorder averaged persistence probability P̅_̅c̅(t) of the global magnetization is found to decay algebraically with an exponent θ_c that we compute analytically in a dimensional expansion in d=4-ϵ. Corrections to Markov process are found to occur already at one loop order and θ_c is thus a novel exponent characterizing this disordered critical point. Our result is

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... oughly compared with Monte Carlo simulations in d=3, which also include a measurement of the initial slip exponent. Taking carefully into account corrections to scaling, θ_c is found to be a universal exponent, independent of the dilution factor p along the critical line at T_c(p), and in good agreement with our one loop calculation.