Plot[Sin[x], {x, -3, 3}, Axes -> True, AxesStyle -> Red]

PolarPlot[θ, {θ, 0, 3 π}, PolarAxes -> True, AxesStyle -> Red]

PolarPlot[θ, {θ, 0, 4 Pi},
  AxesStyle -> {Directive[Thick, Blue], Directive[16, Orange]}
]

Clear[colorPolarAxes]

Options[colorPolarAxes] =
  {PolarAxesStyle -> {}, PolarLabelsStyle -> {}, PolarTicksStyle -> {}};

colorPolarAxes[plot_Graphics, OptionsPattern[]] :=
 ReplaceAll[plot,
  {
   Text[Style[lbl__, {}], pos__] :> Text[Style[lbl, OptionValue[PolarLabelsStyle]], pos],
   Style[Line[def__], {}] :> Style[Line[def], OptionValue[PolarTicksStyle]],
   Circle[options__] :> Style[Circle[options], OptionValue[PolarAxesStyle]]
  }
 ]

colorPolarAxes[
  PolarPlot[θ, {θ, 0, 4 Pi}, PolarAxes -> Automatic, PolarTicks -> {"Degrees", None}],
  PolarAxesStyle -> Orange,
  PolarLabelsStyle -> {Darker@Green, 14, Italic},
  PolarTicksStyle -> {Blue, Thick}
]

PolarPlot[[Theta], {[Theta], 0, 4 Pi},
 PlotStyle -> Directive[Thickness[.006], Black],
 PolarGridLines -> Automatic,
 GridLinesStyle -> Directive[Dashed, Black], PolarAxes -> Automatic,
 PolarTicks -> {"Degrees", Automatic},
 TicksStyle -> Directive[Blue, Thick, 14]]