Make rotate transform like this. And change some options of ListPolarPlot. I modified the PolarTicks option.
rotatePolar[a_List] := Module[{l = Length[a]},
Table[{2 Pi*(i - 1)/l + Pi/2, a[[i]]}, {i, l}]
]
ListPolarPlot[rotatePolar[Reverse[Range[20]]], PolarAxes -> True,
PolarAxesOrigin -> {Pi/2, 20},
PolarTicks -> {Drop[
Table[{i, Mod[i - 90 Degree, 360 Degree]}, {i, 0, 360 Degree,
15 Degree}], -1], Automatic}
]
