Gyrokinetic models of plasma dynamics in tokamak and other fusion devices are characterized by a large range of time scales that span several orders of magnitude. These include transport time scales for kinetic and fluid species, collective wave processes, and collisional processes. High-order implicit-explicit (IMEX) methods allow time-accurate simulations with timesteps determined by the physical processes of interest instead of the fastest timescale in the model. In this talk, we discuss the implementation of semi-implicit, high-order additive Runge-Kutta (ARK) methods for the simulation of magnetized plasmas in the edge-region of a tokamak. We consider a collisional drift-kinetic model for the ion species coupled to a fluid vorticity model for the electrostatic potential, where the Fokker-Planck collisions and parallel current terms introduce stiff timescales in the overall system. The spatially discretized model yields an ordinary differential equation (ODE) of the form d[M(u)]/dt = L(u), where M(u) is a nonlinear function. We propose a modified ARK method that efficiently solves an ODE with a nonlinear left-hand-side operator; a key aspect of our approach is that explicit stages and step completion also require the solution of a nonlinear system of equations. We solve the nonlinear systems with the preconditioned Jacobian-free Newton-Krylov (JFNK) method. An operator-split multiphysics preconditioner is implemented that applies individual, tailored preconditioners for each physical process to the overall implicit right-hand-side in a consistent manner; this avoids the necessity of formulating a monolithic preconditioner for the entire implicit system. This algorithm is implemented in COGENT, a high-order finite-volume code for the simulation of magnetized plasmas on mapped, multiblock grids. We test the performance of our approach and demonstrate high order convergence for simulations representative of tokamak-edge plasmas.