▎ 摘　　要

Laser irradiation, as a versatile tool to tune the topological properties of electronic systems, is under intensive study. Experimentally, a laser irradiation induced anomalous Hall effect in graphene has been observed [J. W. McIver et al., Nat. Phys. 16, 38 (2020)]. Disorder is ubiquitous in real materials, and it has been shown that diagonal disorders, i.e., on-site disorder, can enhance the topological properties of time-periodically driven quantum materials [P. Titum et al., Phys. Rev. Lett. 114, 056801 (2015)]. Here, we investigate circularly polarized laser irradiated graphene with nondiagonal disorders, i.e., disordered tunneling, and find that disorder can induce nontrivial topological properties, characterized by a Bott index and the real-space Chern number. Moreover, we show that one can turn on the laser irradiation nonadiabatically to drive the disordered graphene into a nontrivial topological phase. It is a scheme which is especially interesting for experimental implementations.