We study the two-body and three-body bound states in ultracold atomic mixtures with one of the atoms subjected to an isotropic spin-orbit (SO) coupling. We consider a system of two identical fermions interacting with one SO coupled atom. It is found that there can exist two types of three-body bound states, Efimov trimers and universal trimers. The Efimov trimers are energetically less favored by the SO coupling, which will finally merge into the atom-dimer threshold as increasing the SO coupling strength. Nevertheless, these trimers exhibit a new kind of discrete scaling law incorporating the SO coupling effect. On the other hand, the universal trimers are more favored by the SO coupling. They can be induced at negative s-wave scattering lengths and with smaller mass ratios than those without SO coupling. These results are obtained by both the Born-Oppenheimer approximation and exact solutions from three-body equations.
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