Found a good library "Tweepy (# https://github.com/tweepy/tweepy )"

SampleコードをPython3に対応しました。

Step 1: Install Tweepy

pip install tweepy

Collecting tweepy
  Downloading tweepy-3.5.0-py2.py3-none-any.whl
Requirement already satisfied: requests-oauthlib>=0.4.1 in /Users/aws/Documents/Anaconda/anaconda/lib/python3.6/site-packages (from tweepy)
Requirement already satisfied: requests>=2.4.3 in /Users/aws/Documents/Anaconda/anaconda/lib/python3.6/site-packages (from tweepy)
Requirement already satisfied: six>=1.7.3 in /Users/aws/Documents/Anaconda/anaconda/lib/python3.6/site-packages (from tweepy)
Requirement already satisfied: oauthlib>=0.6.2 in /Users/aws/Documents/Anaconda/anaconda/lib/python3.6/site-packages (from requests-oauthlib>=0.4.1->tweepy)
Installing collected packages: tweepy
Successfully installed tweepy-3.5.0

# !/usr/bin/env python
# encoding: utf-8

import tweepy  
import csv

# Twitter API credentials
consumer_key = ""
consumer_secret = ""
access_key = ""
access_secret = ""


def get_all_tweets(screen_name):
    # Twitter only allows access to a users most recent 3240 tweets with this method

    # authorize twitter, initialize tweepy
    auth = tweepy.OAuthHandler(consumer_key, consumer_secret)
    auth.set_access_token(access_key, access_secret)
    api = tweepy.API(auth)

    # initialize a list to hold all the tweepy Tweets
    alltweets = []

    # make initial request for most recent tweets (200 is the maximum allowed count)
    new_tweets = api.user_timeline(screen_name=screen_name, count=200)

    # save most recent tweets
    alltweets.extend(new_tweets)

    # save the id of the oldest tweet less one
    oldest = alltweets[-1].id - 1

    # keep grabbing tweets until there are no tweets left to grab
    while len(new_tweets) > 0:
        print("getting tweets before %s" % (oldest))

        # all subsiquent requests use the max_id param to prevent duplicates
        new_tweets = api.user_timeline(screen_name=screen_name, count=200, max_id=oldest)

        # save most recent tweets
        alltweets.extend(new_tweets)

        # update the id of the oldest tweet less one
        oldest = alltweets[-1].id - 1

        print("...%s tweets downloaded so far" % (len(alltweets)))

    # transform the tweepy tweets into a 2D array that will populate the csv
    outtweets = [[tweet.id_str, tweet.created_at, tweet.text.encode("utf-8")] for tweet in alltweets]

    # write the csv
    with open('%s_tweets.csv' % screen_name, 'w') as f:
        writer = csv.writer(f)
        writer.writerow(["id", "created_at", "text"])
        writer.writerows(outtweets)

    pass


if __name__ == '__main__':
    get_all_tweets("twitter Username")

参考：　https://gist.github.com/yanofsky/5436496