In this work we investigate the weak deflection angle of light from an exact black hole within nonlinear electrodynamics. First, we calculate the Gaussian optical curvature using the optical spacetime geometry. With the help of modern geometrical methods popularized by Gibbons and Werner, we examine the deflection angle of light from an exact black hole. To do this, we determine the optical Gaussian curvature and apply the Gauss-Bonnet theorem to the optical metric and calculate the leading terms of the deflection angle in the weak-limit approximation. Furthermore, we also study the plasma medium's effect on weak gravitational lensing by an exact black hole. Hence, we determine the effect of nonlinear electrodynamics on the deflection angle in a weak gravitational field.