In 2010 Sarnak formulated the following conjecture on so called Möbius disjointness: for each zero entropy topological system $(T,X)$, each $f\in C(X)$ and $x\in X$, we have $$ \frac1N \sum_{n\leq N}f(T^nx)\mu(n)\to 0 as N\to\infty, $$ where $\mu:\N\to\{-1,0,1\}$ stands for the arithmetic Möbius function. Although, since 2010, the conjecture has been proved in numerous cases, it still remains open. One of the difficulties is that it is unknowm whether if it holds in a uniquely ergodic system $(T,X,\nu)$ then the conjecture holds also in any other uniquely ergodic system $(T',X',\nu')$ such that $(T,\mu)$ and $(T',\mu')$ are measure-theoretically isomorphic. The aim of my talk will be to show that Sarnak's conjecture holds in all uniquely ergodic models of totally ergodic rotations. The talk is based on my joint work with H. Abdalaoui and T. de la Rue.