I'm using the following code for my app and it is working fine, I hope this can help you.
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 {
startActivity(goToMarket);
} catch (ActivityNotFoundException e) {
startActivity(new Intent(Intent.ACTION_VIEW,
Uri.parse("http://play.google.com/store/apps/details?id=" +
context.getPackageName())));
}
This will launch the Play Store with your App & user can promptly review over there.
Make sure, you're popping up correctly the rate us task.