In this paper, I propose a new concept for understanding the role of algorithms in daily life: algorithmic authority. Algorithmic authority is the legitimate power of algorithms to direct human action and to impact which information is considered true. I use this concept to examine the culture of users of Bitcoin, a crypto-currency and payment platform. Through Bitcoin, I explore what it means to trust in algorithmic authority. My study of the Bitcoin community utilizes interview and survey data. I found that Bitcoin users prefer algorithmic authority to the authority of conventional institutions which they see as untrustworthy. However, I argue that Bitcoin users do not have blind faith in algorithms; rather, they acknowledge the need for mediating algorithmic authority with human judgment. I examine the tension between members of the Bitcoin community who would prefer to integrate Bitcoin with existing institutions and those who would prefer to resist integration.