The Beatty Sequence generated by an irrational $r>1$ is $\big(\lfloor nr\rfloor : n>0\big)$, where $\lfloor b\rfloor$ denotes the integer part of a real number $b$. We investigate the expansion of $(\mathbb Z, +,<)$ by the unary subset $B$ consisting of the terms of a Beatty sequence. After explaining that such an expansion is interdefinable with an expansion of $(\mathbb Z,+,<)$ by an orientation/cyclic ordering, we will mention a quantifier elimination result and an axiomatization for the theory of such an expansion. Finally, we mention a decidability result that follows from the axiomatization.