activity_main.xmlMainActivity.java
<?xml version="1.0" encoding="utf-8"?>
<android.support.constraint.ConstraintLayout xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    android:layout_width="match_parent"
    android:layout_height="match_parent"
    tools:context="com.codinginflow.ratemeexample.MainActivity">

    <Button
        android:layout_width="wrap_content"
        android:layout_height="wrap_content"
        android:onClick="rateMe"
        android:text="Rate Me!"
        app:layout_constraintBottom_toBottomOf="parent"
        app:layout_constraintLeft_toLeftOf="parent"
        app:layout_constraintRight_toRightOf="parent"
        app:layout_constraintTop_toTopOf="parent" />

</android.support.constraint.ConstraintLayout>

package com.codinginflow.ratemeexample;

import android.content.ActivityNotFoundException;
import android.content.Intent;
import android.net.Uri;
import android.support.v7.app.AppCompatActivity;
import android.os.Bundle;
import android.view.View;

public class MainActivity extends AppCompatActivity {

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
    }

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