The PHP Imagick way would be to test the image orientation and rotate/flip the image accordingly:
function autorotate(Imagick $image)
{
    switch ($image->getImageOrientation()) {
    case Imagick::ORIENTATION_TOPLEFT:
        break;
    case Imagick::ORIENTATION_TOPRIGHT:
        $image->flopImage();
        break;
    case Imagick::ORIENTATION_BOTTOMRIGHT:
        $image->rotateImage("#000", 180);
        break;
    case Imagick::ORIENTATION_BOTTOMLEFT:
        $image->flopImage();
        $image->rotateImage("#000", 180);
        break;
    case Imagick::ORIENTATION_LEFTTOP:
        $image->flopImage();
        $image->rotateImage("#000", -90);
        break;
    case Imagick::ORIENTATION_RIGHTTOP:
        $image->rotateImage("#000", 90);
        break;
    case Imagick::ORIENTATION_RIGHTBOTTOM:
        $image->flopImage();
        $image->rotateImage("#000", 90);
        break;
    case Imagick::ORIENTATION_LEFTBOTTOM:
        $image->rotateImage("#000", -90);
        break;
    default: // Invalid orientation
        break;
    }
    $image->setImageOrientation(Imagick::ORIENTATION_TOPLEFT);
}
The function might be used like this:
$img = new Imagick('/path/to/file');
autorotate($img);
$img->stripImage(); // if you want to get rid of all EXIF data
$img->writeImage();