Rawls (and though I do not fault him for this, I do question the point of it in the end) says that his theory counts as pro-autonomy and pro-objectivity (AToJ, sec. 78). The objectivity-friendly side of these things, he imputes to the requirement that we take up the perspective of others to an extent, though why he didn't just say "intersubjective" about it, then, I don't know (perhaps the word wasn't so current at the time). To the extent that there is something decisively contra relativism/moral relativity, here, it is that he cannot countenance a perspective based on ignoring or destroying any or all other perspectives.
However, AToJ is a long and involved book so there are some interesting considerations that crop up throughout, that pertain to this issue of whether and to what extent an objective, but relative, justification for (parts of) the theory might obtain. First, consider the section about tolerating the intolerant (35). Rawls says that even if it would be quite hypocritical for an intolerant sect to complain about its "rights" being violated, more dispassionate nonsectarians could still object to such violations, and not even directly on the sect's behalf but in the light of general principles. Ultimately Rawls argues that physical suppression of a sect is justified only if the sect is physically dangerous enough to the stability of the well-ordered society in which it has unfortunately emerged.
Or consider Rawls' invocation of the plurality, both intrapersonal and interpersonal, of "final ends." He says (sec. 39):
... liberty of conscience and freedom of thought should not be founded on philosophical or ethical skepticism, nor on indifference to religious and moral interests. The principles of justice define an appropriate path between dogmatism and intolerance on the one side, and a reductionism which regards religion and morality as mere preferences on the other.
For Rawls, it is necessary that we be licensed to invest a real sense of importance in our "final ends," even if not absolutely all such ends are admissible into a well-ordered society.
Another relativism/relativity-friendly moment comes when Rawls suggests that a justifiable political economy can be variously implemented depending on historical/geographical variations (sec. 42), so that some countries can justify adopting or maintaining a capitalist spirit, others a socialist one.
One way to frame the whole issue, then, is to look at a first-order relativism first, and then look at Rawls' principles of justice as second-order and partly nonrelative over divergent first-order claims. Rawls' tone throughout AToJ is so considerate, he's so prone to amorphously suggest that everything he's saying is somehow wrong in the end anyway, perhaps, that it's hard to see him as trying to argue from a strictly absolutist perspective himself. One might say that if political science is (meant to be) the art of solving problems of moral disagreement, it is a second-order ethical science, but one that requires, then, that participants in disagreements be open to the possibility of being variously wrong. When relativism is used as an excuse to justify one's decision so as to short-circuit debate over the possibility of being mistaken about one's justifications, it is not very consonant at all with Rawls' attitude and intent; this doesn't rule out, however, the possibility of ineliminable morally relativistic thought processes, as themselves justified to some, even a majority, extent.