php composer.phar create-project --prefer-dist --stability=dev yiisoft/yii2-app-basic basic

// ...
"require": {
 "php": ">=5.4.0",
 "hybridauth/hybridauth": "dev-master",
 "FortAwesome/Font-Awesome": "*", // <- 这里
 "yiisoft/yii2": "*",
 "yiisoft/yii2-swiftmailer": "*",
 "yiisoft/yii2-bootstrap": "*",
 "yiisoft/yii2-debug": "*",
 "yiisoft/yii2-gii": "*"
},
// ...

php composer.phar update

namespace assets;
use yii\web\AssetBundle;
class FontAwesomeAsset extends AssetBundle
{
 // 下面这些资源文件并不在 web 目录下，浏览器无法直接访问。所以我们需要
 // 指定 sourcePath 属性。注意 @vendor 这个 alias，表示 vender 目录
 public $sourcePath = '@vendor/fortawesome/font-awesome';
 public $css = [
  'css/font-awesome.css',
 ];
}

// 这两句直接写在那一页的 view 里
use assets\FontAwesomeAsset;
FontAwesomeAsset::register($this);

class AppAsset extends AssetBundle
{
 public $basePath = '@webroot';
 public $baseUrl = '@web';
 public $css = [
  'css/site.css',
 ];
 public $js = [
 ];
 public $depends = [
  'yii\web\YiiAsset',
  'yii\bootstrap\BootstrapAsset',
  // 在这里加上我们的 FontAwesomeAsset 包类
  'assets\FontAwesomeAsset'
 ];
}