  The critical behavior of the random transverse-field Ising model in finite
dimensional lattices is governed by infinite disorder fixed points, several
properties of which have already been calculated by the use of the strong
disorder renormalization group (SDRG) method. Here we extend these studies and
calculate the connected transverse-spin correlation function by a numerical
implementation of the SDRG method in $d=1,2$ and $3$ dimensions. At the
critical point an algebraic decay of the form $\sim r^{-\eta_t}$ is found, with
a decay exponent being approximately $\eta_t \approx 2+2d$. In $d=1$ the
results are related to dimer-dimer correlations in the random AF XX-chain and
have been tested by numerical calculations using free-fermionic techniques.
