Is there a area code that is the number 010?

There is no telephone area code 010 in the United States, nor in North America. (The US is part of a unified numbering plan for North America, including Canada and 18 island nations and territories in or near the Caribbean.)

01 is the prefix for operator-assisted international calls from North America, but it can never be followed by another zero.

There are codes beginning with 101, including some beginning with 1010, used to select a particular long distance company on a per-call basis. For example, you might dial 101xxxx-1-999-555-0123.