With the fast approach of the end of silicon scaling and existing problems such as the Von-Neumann bottleneck, alternative computing paradigms are in demand. In-Memory Computation (IMC) is one of the most promising solutions, and memristive technology is one of the best platforms for that purpose. Many logic families have been proposed to enable memristive IMC, among which stateful logic family stands out thanks to its minimal power consumption and simplicity. In this work, to complement existing works, we propose the first stateful crossbar-compatible XOR atomic logic operation that requires only one cycle for its completion. That is two times faster than the current minimum required time for performing XOR (which is two cycles) using other atomic operations in comparable memristive stateful logic families. We show that in an example case of an adder, by taking advantage of the proposed Single-cycle In-memristor XOR (SIXOR), up to 4.5x speed-up can be achieved compared to other State-of-the-Art (SoA) stateful adders. The gained speed-up scales up in more complex systems and calculations that use XOR.