Fusion of $q$-tensor operators: quasi-Hopf-algebraic point of view

We discuss the fusion of tensor operators for $U_q(\mathscr J)$ by means of the $R$-matrix approach. The problem is reduced to construction of the twisting element $\mathscr J$ which appears in Drinfeld's description of quasi-Hopf algebras. The discussion is illustrated by explicit calculations for the case of $U_q(sl(2))$.