Install software:

opkg update #updates the available packages list
opkg install python-openssl #adds ssl support to python
opkg install distribute #it contains the easy_install
easy_install twython
nano  /mnt/sda1/yuntwitter.py
#!/usr/bin/python
from twython import Twython
import sys
messagetotwitter=sys.argv[1]
APP_KEY='Your Twitter APP_KEY'
APP_SECRET='Your Twitter APP_SECRET'
OAUTH_TOKEN='Your Twitter OAUTH_TOKEN'
OAUTH_TOKEN_SECRET='Your Twitter OAUTH_TOKEN_SECRET'
twitter = Twython(APP_KEY, APP_SECRET, OAUTH_TOKEN, OAUTH_TOKEN_SECRET)
twitter.update_status(status=messagetotwitter)
chmod 755 /mnt/sda1/yuntwitter.py

Test tweets:

/mnt/sda1/yuntwitter.py "I'm tweeting from Arduino!"

ATmega32u4 Code:

#include <Process.h>
void setup() {
 Bridge.begin();  // Initialize Bridge
}
void loop() {
 Process p;              
 p.begin("/mnt/sda1/yuntwitter.py");      
 p.addParameter("I'm tweeting from Arduino Yun!"); 
 p.run();
 while(1){};  //run once
}