自从这个答案以来，很多时间已经过去了，现在有一种方法可以将谷歌播放审查窗口附加到你的应用程序

https://developer.android.com/guide/playcore/in-app-review

// In your app’s build.gradle file:
...
dependencies {
    // This dependency is downloaded from the Google’s Maven repository.
    // So, make sure you also include that repository in your project's build.gradle file.
    implementation 'com.google.android.play:core:1.10.0'

    // For Kotlin users also add the Kotlin extensions library for Play Core:
    implementation 'com.google.android.play:core-ktx:1.8.1'
    ...
}

然后，当您想要显示速率弹出时

final ReviewManager manager = ReviewManagerFactory.create(context);
final Task<ReviewInfo> request = manager.requestReviewFlow();
request.addOnCompleteListener(task -> {
    if (task.isSuccessful()) {
        // We can get the ReviewInfo object
        ReviewInfo reviewInfo = task.getResult();
        Task<Void> flow = manager.launchReviewFlow(context, reviewInfo);
flow.addOnCompleteListener(task -> {
    // The flow has finished. The API does not indicate whether the user
    // reviewed or not, or even whether the review dialog was shown. Thus, no
    // matter the result, we continue our app flow.
});
    } else {
        // There was some problem, log or handle the error code.
        @ReviewErrorCode int reviewErrorCode = ((TaskException) task.getException()).getErrorCode();
    }
});

正如在评论中所说的，API不会让你知道用户给出了什么评级

谷歌也有严格的指导方针使用这个api，频率你被允许显示窗口是有限的，也不允许诱导用户给你一个好的评价。你可以在上面的链接中查看完整的文档和指南

你可以使用这个简单的代码来评估你的应用程序在你的活动。

try {
    Uri uri = Uri.parse("market://details?id=" + getPackageName());
    Intent goToMarket = new Intent(Intent.ACTION_VIEW, uri);
    startActivity(goToMarket);
} catch (ActivityNotFoundException e) {
    startActivity(new Intent(Intent.ACTION_VIEW,
    Uri.parse("http://play.google.com/store/apps/details?id=" + getPackageName())));
}

你可以用这个，它对我有用

public static void showRateDialogForRate(final Context context) {
    AlertDialog.Builder builder = new AlertDialog.Builder(context)
            .setTitle("Rate application")
            .setMessage("Please, rate the app at PlayMarket")
            .setPositiveButton("RATE", new DialogInterface.OnClickListener() {
                @Override
                public void onClick(DialogInterface dialog, int which) {
                    if (context != null) {
                        ////////////////////////////////
                        Uri uri = Uri.parse("market://details?id=" + context.getPackageName());
                        Intent goToMarket = new Intent(Intent.ACTION_VIEW, uri);
                        // To count with Play market backstack, After pressing back button,
                        // to taken back to our application, we need to add following flags to intent.
                        goToMarket.addFlags(Intent.FLAG_ACTIVITY_NO_HISTORY |
                                Intent.FLAG_ACTIVITY_CLEAR_WHEN_TASK_RESET |
                                Intent.FLAG_ACTIVITY_MULTIPLE_TASK);
                        try {
                            context.startActivity(goToMarket);
                        } catch (ActivityNotFoundException e) {
                            context.startActivity(new Intent(Intent.ACTION_VIEW,
                                    Uri.parse("http://play.google.com/store/apps/details?id=" + context.getPackageName())));
                        }


                    }
                }
            })
            .setNegativeButton("CANCEL", null);
    builder.show();
}

前提是你同时在谷歌Play Store和Amazon Appstore发布应用。我还处理过用户(尤其是中国用户)既没有应用商店又没有浏览器的情况。

public void goToMyApp(boolean googlePlay) {//true if Google Play, false if Amazone Store
    try {
       startActivity(new Intent(Intent.ACTION_VIEW, Uri.parse((googlePlay ? "market://details?id=" : "amzn://apps/android?p=") +getPackageName())));
    } catch (ActivityNotFoundException e1) {
        try {
            startActivity(new Intent(Intent.ACTION_VIEW, Uri.parse((googlePlay ? "http://play.google.com/store/apps/details?id=" : "http://www.amazon.com/gp/mas/dl/android?p=") +getPackageName())));
        } catch (ActivityNotFoundException e2) {
            Toast.makeText(this, "You don't have any app that can open this link", Toast.LENGTH_SHORT).show();
        }
    }
}

从现在开始，你可以使用谷歌的应用评级功能。

这里是Kotlin/Java集成的官方指南

谷歌Play In-App Review API允许您提示用户提交Play Store评级和评论，而无需离开您的应用程序或游戏。 通常，应用内部审查流程(见图1)可以在 在你的应用程序的用户旅程的任何时间 用户可以使用1到5星系统对你的应用进行评级 添加可选注释。一旦提交，审查将被发送到 播放商店和最终显示。

Play Store评分

 btn_rate_us.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View v) {
                Uri uri = Uri.parse("market://details?id=" + getPackageName());
                Intent goToMarket = new Intent(Intent.ACTION_VIEW, uri);
                // To count with Play market backstack, After pressing back button,
                // to taken back to our application, we need to add following flags to intent.
                goToMarket.addFlags(Intent.FLAG_ACTIVITY_NO_HISTORY |
                        Intent.FLAG_ACTIVITY_NEW_DOCUMENT |
                        Intent.FLAG_ACTIVITY_MULTIPLE_TASK);
                try {
                    startActivity(goToMarket);
                } catch (ActivityNotFoundException e) {
                    startActivity(new Intent(Intent.ACTION_VIEW,
                            Uri.parse("http://play.google.com/store/apps/details?id=" + getPackageName())));
                }
            }
        });