Rotational spectra of the Ar-SH((2)Pi (i)) radical complex and its deuterated species have been studied using a Fourier-transform microwave spectrometer. The complexes are produced in a supersonic free jet using a pulsed discharge of H2S or D2S diluted in Ar. R-branch transitions in the lower spin component (Omega =3/2) for the linear (2)Pi (i) radical were observed for J"=1.5-7.5 in the 8-26 GHz region, in which the parity doublings and hyperfine splittings associated with the H/D nuclei have been observed. Effective rotational constants for Ar-SH and Ar-SD are determined to be 1569.660(3) and 1567.723(4) MHz, respectively, using an effective (2)Pi Hamiltonian including hyperfine terms. An effective centrifugal distortion constant, D, has been determined to be negative. A two-dimensional intermolecular potential energy surface for the Ar-SH((2)Pi (i)) complex has been derived from a least-squares fitting of the observed rotational transitions, where several parameters are constrained to the values from an ab initio calculation at the RCCSD(T)/aug-cc-pVQZ level. The average potential turned out to be fairly isotropic with two shallow minima corresponding to the linear Ar . . . SH and Ar . . . HS configurations, among which the former is 7.2 cm(-1) more stable than the latter. The determined equilibrium distance between Ar and the SH center-of-mass is 3.791 Angstrom at the Ar . . . SH global minimum configuration. The vibrational ground state is located above the barrier of only about 20 cm(-1) between the two minima, and its wave function is widely spread along the bending coordinate. The negative sign of the effective D constant is well explained by the enhancement of the probability at the linear Ar . . . SH configuration by the centrifugal force, which results in a decrease of the vibrationally averaged Ar-SH intermolecular distance.