The nontrivial magnetoopitcal effects are predicted to arise at the visible frequency range for monolayer transition metal dichalcogenides upon the application of magnetic exchange interactions. However, their magnetoopitcal rotation angles at the terahertz frequency range are always low, which hinders their practical applications in the terahertz magnetoopitcal devices. In this letter, we theoretically demonstrate that the magnetoopitcal effects of monolayer transition metal dichalcogenides at the terahertz frequency range can be enhanced and controlled via introducing the Rashba spin orbit coupling, whose rotation angles are comparable with those of conventional bulky magnetic materials. Such an effect originates from the change of spin-up and spin-down bands in the band structures of monolayer transition metal dichalcogenides when the Rashba spin orbit coupling and magnetic exchange interaction coexist, which enables the spin-flip intraband optical transitions and thus generates the terahertz magnetoopitcal responses. Our results open up possibilities for the use of Rashba spin orbit coupling to generate as well as control the magnetoopitcal effects in two-dimensional layered materials.