Android - Rotate image inside the button

The simplest method would be to rotate the entire button (and as Frank N. Stein suggested in the comments, an ImageButton is probably best suited, although there's nothing to stop you from using a different widget).

There are several ways to rotate the button, but a ViewPropertyAnimator is again likely the most straightforward:

button.setOnClickListener(new View.OnClickListener() {
    @Override
    public void onClick(View v) {
        float deg = button.getRotation() + 180F;
        button.animate().rotation(deg).setInterpolator(new AccelerateDecelerateInterpolator());
    }
});

Edit: By the way, if you want the arrow to reverse its original animation, you could instead try:

float deg = (button.getRotation() == 180F) ? 0F : 180F;

instead of float deg = button.getRotation() + 180F;

You can set bitmap as background in button.

Matrix matrix = new Matrix();

matrix.postRotate(90);

Bitmap scaledBitmap = Bitmap.createScaledBitmap(bitmapOrg,width,height,true);

Bitmap rotatedBitmap = Bitmap.createBitmap(scaledBitmap , 0, 0, scaledBitmap .getWidth(), scaledBitmap .getHeight(), matrix, true);

First take bitmap from any source and then rotate it and then set it as background in button.

BitmapDrawable bdrawable = new BitmapDrawable(context.getResources(),bitmap);
button.setBackground(bdrawable);