  We study the anomalous dimensions of operators in the scalar sector of
\beta-deformed ABJ(M) theories. We show that the anomalous dimension matrix at
two-loop order gives an integrable Hamiltonian acting on an alternating SU(4)
spin chain with the spins at odd lattice sides in the fundamental
representation and the spins at even lattices in the anti-fundamental
representation. We get a set of $\beta$-deformed Bethe ansatz equations which
give the eigenvalues of Hamiltonian of this deformed spin chain system. Based
on our computations, we also extend our study to non-supersymmetric
three-parameter $\gamma$-deformation of ABJ(M) theories and find that the
corresponding Hamiltonian is the same as the one in \beta-deformed case at
two-loop level in the scalar sector.
