Dilute nickel alloys charged with hydrogen are known to exhibit an internal friction peak, which is attributed to the reorientation of hydrogen-solute atom pairs. In order to determine the geometrical configuration of the pair, we have studied anisotropy of the relaxation strength in dilute Ni-Ti-H alloy single crystals by low-frequency internal friction measurements. The orientation dependence of the peak height suggests that the defect symmetry is 〈111〉 trigonal. One of the possible configurations is the Ti-H pair in which hydrogen occupies the second neighbour octahedral sites around the substitutional solute atom. The peak has been found to be suppressed by an external magnetic field, indicating that magneto-elastic effects play an important role.