As mentioned by Alko, you need root access to write to the directory where pip stores the packages.
You can type:
sudo su
in the terminal and then type:
pip install tweepy
Alternatively, you can use virtualenv:
"What if you can't install packages into the global site-packages directory? For instance, on a shared host.
In all these cases, virtualenv can help you. It creates an environment that has its own installation directories, that doesn't share libraries with other virtualenv environments (and optionally doesn't access the globally installed libraries either)."
Basically, it will allow you to create isolated environments for each of your python projects and will allow you to sidestep the permissions issue you are having.
For a good explanation see: Installing Python on Mac OS X: virtualenv