How to rotate a graph with a locator?

(1) You can use Locator as a graphics primitive and rotate all the graphics primitives, and
(2) use Experimental`AngularSlider to control the angle:

Manipulate[Graphics[Rotate[{Line[{{0, 0}, p}], Locator[Dynamic[p]]}, θ, {0, 0}], 
   PlotRange -> 2, ImageSize -> Small],
 {{p, {1, 0}}, None},
 {{θ, 0, ""}, 0, 2 π, Labeled[Experimental`AngularSlider[#, {0, 2 Pi}, 
     Experimental`BoundaryAction -> None], Row[{"θ = ", #}], Top] &}, 
 Deployed -> True]

To prevent the locator from going out of plot area after rotation, we can use the second argument of Dynamic to restrict the locator to stay within a disk of radius 2:

Manipulate[Graphics[Rotate[{Line[{{0, 0}, p}], 
    AbsolutePointSize[10], Red, Point[p], 
    Locator[Dynamic[p, (p = If[Norm[#] < 2, #, 2 Normalize[#]];) &], None]}, 
    θ, {0, 0}], PlotRange -> 2,  ImageSize -> Small],
 {{p, {1, 0}}, None}, 
 {{θ, 0, ""}, 0, 2 π, Labeled[Experimental`AngularSlider[#, {0, 2 Pi}, 
     Experimental`BoundaryAction -> None], Row[{"θ = ", #}], Top] &}, 
 Deployed -> True]

Update: If you want the two controls linked so that the angle is updated as the locator moves, change Locator[...] to

Locator[Dynamic[p, (p = If[Norm[#] < 2, #, 2 Normalize[#]]; θ = ArcTan @@ p) &], None]