The kinetic theory of twisted wave instability is developed for the nonthermal dusty plasmas in the presence of helical electric field carrying orbital angular momentum (OAM). The Laguerre Gaussian (LG) mode function is employed to decompose the mode into its longitudinal and azimuthal components. The longitudinal component illustrates the spatial while the azimuthal component describes the phasor variation of the wave. The dielectric functions of quasi-electrostatic dust ion acoustic (DIA) and dust acoustic (DA) twisted modes are obtained and solved analytically to calculate the growth rates. The numerical results are also shown pictorially.