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

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.

Reference; add_user_meta

And added information will get by get_user_meta