We obtain global Strichartz estimates for the solutions u of the wave equation ( ∂ t 2 − Δ x + V ( t , x ) ) u = F ( t , x ) for time-periodic potentials V ( t , x ) with compact support with respect to x. Our analysis is based on the analytic properties of the cut-off resolvent R χ ( z ) = χ ( U ( T ) − z I ) −1 ψ 1 , where U ( T ) = U ( T , 0 ) is the monodromy operator and T > 0 the period of V ( t , x ) . We show that if R χ ( z ) has no poles z ∈ C , | z | ⩾ 1 , then for n ⩾ 3 , odd, we have a exponential decal of local energy. For n ⩾ 2 , even, we obtain also an uniform decay of local energy assuming that R χ ( z ) has no poles z ∈ C , | z | ⩾ 1 , and R χ ( z ) remains bounded for z in a small neighborhood of 0.