How can I rotate a Container widget in 2D around a specified anchor point?

Per Ian's advice, I gave the following a try. It appears to work, at least in my limited testing.

The container is nested within a Transform widget. Using alignment allows one to adjust the transform-origin in relative terms, i.e., in the center, the top left, etc.

var container = new Container (
  child: new Stack (
    children: [
      new Image.asset ( // background photo
        "assets/texture.jpg",
        fit: ImageFit.cover,
      ),
      new Center (
        child: new Transform (
          child: new Container (
            child: new Text (
              "Lorem ipsum",
              style: new TextStyle(
                color: Colors.white,
                fontSize: 42.0,
                fontWeight: FontWeight.w900,
              )
            ),
            decoration: new BoxDecoration (
              backgroundColor: Colors.black,
            ),
            padding: new EdgeInsets.fromLTRB(16.0, 16.0, 16.0, 16.0),              
          ),
          alignment: FractionalOffset.center, // set transform origin
          transform: new Matrix4.rotationZ(0.174533), // rotate -10 deg
        ),
      ),
    ],
  ),
  width: 400.0,
  height: 200.0,
);

In flutter 2.2

Use Transform:

Transform(
    transform: Matrix4.rotationZ(...),
    alignment: FractionalOffset.center,
    child: Container(...)

Or set transformAlignment value in Container:

Container(
    ...
    transform: Matrix4.rotationZ(...),
    transformAlignment: Alignment.center,
)

You can use RotatedBox Widget to rotate any widget:

RotatedBox(
    quarterTurns: 3,
    child: Container(
        color:Colors.red
    ),
),

Apply a translation (to and from the fulcrum) before and after the rotation.

You can create yourself a little widget that does this, and thus solve your other problem at the same time (hiding the Matrix4).