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The decay of (disorder‐averaged) static spin correlation functions at T=0 for the one‐dimensional spin‐1/2 XXZantiferromagnet with uniform longitudinal coupling JΔ and random transverse coupling Jλ i is investigated by numerical calculations for ensembles of finite chains. At Δ=0 (XXmodel) the calculation is based on the Jordan‐Wigner mapping to free lattice fermions for chains with up to N=100 sites. At Δ≠0 Lanczos diagonalizations are carried out for chains with up to N=22 sites. The longitudinal correlation function 〈S z 0 S z r 〉 is found to exhibit a power‐law decay with an exponent that varies with Δ and, for nonzero Δ, also with the width of the λ i ‐distribution. The results for the transverse correlation function 〈S x 0 S x r 〉 show a crossover from power‐law decay to exponential decay as the exchange disorder is turned on.