No it can't. Turbulence does not introduce net-angular momentum. It just (re)distributes it. And the scale on which that "mixing" can happen is limited (essentially the speed of sound is smaller than the expansion of the universe in the early universe). So on large enough scale, it (~any vector value) must be add up to ~zero (up to the initialisation uncertainties). Or one of our fundamental assumptions is wrong. And that's why this is so interesting