Can a Boolean circuit be considered an algorithm?
Have a look at Turing-completeness and the Church-Turing thesis (CT). Basically, CT is saying that everything that is computable, is computable on a Turing machine. Many different models of computation are known to be equivalent to the Turing machine. Even if you are considering something esoteric you came up with yourself, if what you have is Turing-complete, you can claim that you really do have an algorithm.

A circuit is a non-uniform model of computation, meaning that different size circuit compute things for different size inputs. A Turing machine on the other hand is a uniform model, so it's used for all input lengths. Given a Turing machine, one can construct a Boolean circuit that is able to simulate all its computation if we put a bound on the Turing machine's memory. Also, given a circuit, we can build a Turing machine that simulates the circuit.