Can I be an anarchist and a muslim at the same time. I believe that no authority has the right to rule over me if not an infallible, hence that makes me an anarchist?

No in Islamic Law, we have a process in place in the absence of an Imam. For instance, some scholars state the a jurist rules or at least he oversees the way a government is ruled. Some believe that just believers should play a role in that.
In any case, if people become anarchists, then there would be complete chaos in society and it would become dangerous. There must be some sort of law and order.