It's not possible to do automatically, you can use the Rotate tool and then rotate (or with the Selection tool).
Related post
You can also use this nice script by Michael Prewitt on Github which does it for you (it rotates everything 90°)
// Rotate Artboard 90 degrees clockwise
// INSTALLATION:
// Install in /Applicatons/[Illustrator folder]/Presets/en_US/Scripts
// DESCRIPTION:
// Rotate the artboard in 90 degree increments.
// SOURCES:
// https://forums.adobe.com/message/9074536#9074536
// Make sure we have an open document, or else open one
if( app.documents.length == 0 ) {
fileToProcess = File.openDialog();
app.open(fileToProcess);
}
var doc = app.activeDocument;
var currentArtboard = doc.artboards.getActiveArtboardIndex();
var currentArtboardRect = doc.artboards[currentArtboard].artboardRect; // Rect, which is an array;
var currentLeft = currentArtboardRect[0];
var currentTop = currentArtboardRect[1];
var currentRight = currentArtboardRect[2];
var currentBottom = currentArtboardRect[3];
var currentWidth = Math.abs( currentRight - currentLeft );
var currentHeight = Math.abs( currentBottom - currentTop );
var centerX = currentLeft + (currentWidth/2);
var centerY = currentTop - (currentHeight/2); // Y axis is inverted
var newArtboardRect = [];
var newWidth = currentHeight;
var newHeight = currentWidth;
// Rotate the artboard 90 degrees
newArtboardRect[0] = centerX-(newWidth/2);
newArtboardRect[1] = centerY+(newHeight/2); // Y axis is inverted
newArtboardRect[2] = centerX+(newWidth/2);
newArtboardRect[3] = centerY-(newHeight/2); // Y axis is inverted
doc.artboards[currentArtboard].artboardRect = newArtboardRect;
// Set ruler origin to center, rotate everything around custom pivot, reset the ruler
var currentOrigin = [ newArtboardRect[0], newArtboardRect[1] ];
// currentArtboard.rulerOrigin = currentOrigin;
doc.rulerOrigin = currentOrigin;
// currentArtboard.rulerOrigin = [newWidth/2,newHeight/2];
doc.rulerOrigin = [newWidth/2,newHeight/2];
// alert("Rotation X Y coords are " + newWidth/2 + ", " + newHeight/2 + ".");
// CURRENT BUG:
// Setting the rulerOrigin does NOT work
var pItems = doc.pageItems;
for(var i = 0;i < pItems.length;i++){
pItems[i].rotate(270,true,true,true,true,Transformation.DOCUMENTORIGIN);
}
doc.rulerOrigin = currentOrigin;
Note: The current release is extremely buggy. It works (sometimes!) for very simple graphics. However, there are two significant bugs: (1) It will sometimes scatter objects during the rotation of the artboard; this happens quite often with more complex artwork, and occasionally with artwork that seems simple. (2) It will sometimes rotate the artboard 180 degrees instead of 90.
