'com.google.android.gms.common.api.GoogleApiClient' is deprecated

Yeah GoogleApiClient has been deprecated.

As per the documentation:

When you want to make a call to one of the Google APIs provided in the Google Play services library (such as Google Sign-in and Drive), you need to create an instance of one the API client objects, which are subclasses of GoogleApi

Particularly for the authentication api, you now need to use GoogleSignInClient.

    // Configure sign-in to request the user's ID, email address, and basic
    // profile. ID and basic profile are included in DEFAULT_SIGN_IN.
    GoogleSignInOptions gso = new GoogleSignInOptions.Builder(GoogleSignInOptions.DEFAULT_SIGN_IN)
            .requestEmail()
            .build();

    // Build a GoogleSignInClient with the options specified by gso.
    mGoogleSignInClient = GoogleSignIn.getClient(this, gso);

You may refer following documentations for more details:

• Integrating Google Sign-In into Your Android App
• Moving Past GoogleApiClient