Memristor is a new nonlinear circuit element. It is a special case of memristive systems. It has a charge-dependent resistance and a frequency dependent hysteresis curve when excited with an AC source. It has been claimed as the fourth fundamental circuit element in 1971 and a solid-state thin film behaving as a memristor system is found in 2008. Following this discovery, memristor-based memories, neurons, ANN circuits, chaotic sources, analog filters and oscillators have become a hot research area and, if one day memristor becomes commercially available, it may give way to new types of analog applications due to its tunable resistance. In this paper, a memristor-based phase shifter circuit is examined for the first time in literature.