Carr appears to think the internet has become an extremely valuable tool to society today. He recognizes how it has become part of everyday life and how it has affected everyone. Since Carr views this as a tool to society today, in my judgment, that would declare him a believer.
Although I believe he is considered a believer, there are some aspects of this article that I suppose would deem him a doubter as well. He has many well-developed ideas and viewpoints, which is not a particular quality of the believer, where everything is automatically considered to be true. Nicholas Carr, in my opinion, is both a believer and a doubter.