You can take below steps as guideline.
After logged in user, you can display one form to add twitter URL.
after submitting that form by user, add this form info by using `add_user_meta` for logged in user.

check `add_user_meta` in following link.
http://codex.wordpress.org/Function_Reference/add_user_meta

And added information will get by `get_user_meta` function,for this follow below link.
http://codex.wordpress.org/Function_Reference/get_user_meta