VectorPlot[
 Normalize[{
    Cos[ArcTan[y, x]] + 0.33*Sin[ArcTan[y, x]], -Sin[ArcTan[y, x]] +
    0.33*Cos[ArcTan[y, x]]
   }],

 (* Range *)
 {x, -3, 3}, {y, -3, 3},

 (* Style *)
 VectorStyle -> Orange,
 VectorScale -> {Scaled[0.04], Scaled[0.04]},
 Background -> RGBColor[0.2, 0.2, 0.5],
 Frame -> False,
 Prolog -> {Opacity[0.24], White, Disk[]}
 ]