There are large attractors, for instance (in order of increasing mass and decreasing proximity) Virgo, the Great Attractor, and the Shapley attractor) There is some net rotation about each of these, but no disk to speak of as far as I know.
The universe, if not finite in size, is incapable of rotation. Rotation around an attractor only works given the causal reach of the mass, so nothing outside our visible universe can have an influence on our motion, and thus we cannot rotate around it, however slowly.
Secondly, any finite angular rate multiplied by unbounded distance would have distant objects moving faster than light in a coordinate system where such motion is impossible.
Of course it's allowed in other kinds of coordinate systems. Relative to my house, the universe rotates overhead, and anything as far away as Neptune or more likely moves faster than c, but that's just a property of such a coordinate system. Nothing out by Neptune is capable of being stationary either in such a frame