Graphics[Cases[Plot[Sin[x],{x,0,2Pi}],Line[x_]:>Arrow[Line[x]],\[Infinity]]]
Graphics[Cases[ParametricPlot[{Sin[u],Sin[2u]},{u,0,2Pi}],Line[x_]:>Arrow[Line[x]],\[Infinity]]]
Graphics[Cases[Plot[0.3x^2-1x,{x,-3,3}],Line[x_]:>Arrow[Line[x]],\[Infinity]]]
Graphics[Cases[Plot[{Sin[x],Sin[2x]},{x,0,2Pi}],Line[x_]:>Arrow[Line[x]],\[Infinity]]]
This will work for plot functions that do not produce GraphicsComplex objects: ParametricPlot with parametric curves, Plot, PolarPlot, et cetera...