The rotational alignment of the dissociative adsorption of Hz on the Cu(lll) surface has been studied by a six-dimensional quantum dynamics simulation. The theoretical rotational alignment is in excellent agreement with the experimental measurement of Hou et al. [Science 277, 80 (1997)]. The translational energy threshold of the dissociation is found to increase with increase of rotational quantum number j then to decrease after j = 4 or 5. No substantial difference in the dependence of rotational alignment on the excess translational energy has been found between the dissociation of H-2 and D-2 on the Cu(lll) surface. The variation of rotational alignment as a function of excess translational energy is almost independent of the rovibrational level (v,j) of the initial state. The theoretical study further predicts that the rotational alignment curve (a function of translational energy) would first shift toward high translational energy with increasing j, then shift back toward low translational energy after j=5.