i = Import@"https://i.sstatic.net/8I3B1.jpg"
f[{{tmin_, tmax_}, {rmin_, rmax_}}, ___] :=
Module[{l = Join[{{0, 0}, {Cos@tmin, Sin@tmin}},
Table[{Cos[t], Sin[t]}, {t, tmin, tmax, (tmax - tmin)/30}],
{{Cos@tmax, Sin@tmax}}]},
{Texture[i], EdgeForm[], Polygon[l, VertexTextureCoordinates ->
1/2 Transpose[Transpose[l] + {1, 1}]]}]
Framed@PieChart[{1, 2, 3, 4, 5, 6}, ChartElementFunction -> f]
