The realization of the quantum anomalous Hall (QAH) effect without magnetic doping attracts intensive interest since magnetically doped topological insulators usually possess inhomogeneity of ferromagnetic order. Here, we propose a different strategy to realize intriguing QAH states arising from the interplay of light and non-magnetic disorder in two-dimensional topologically trivial systems. By combining the Born approximation and Floquet theory, we show that a time-reversal invariant disorder-induced topological insulator, known as the topological Anderson insulator (TAI), would evolve into a time-reversal broken TAI and then into a QAH insulator by shining circularly polarized light. We utilize spin and charge Hall conductivities, which can be measured in experiments directly, to distinguish these three different topological phases. This work not only offers an exciting opportunity to realize the high-temperature QAH effect without magnetic orders, but also is important for applications of topological states to spintronics.
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